Transcript Penentuan Jarak dalam Astronomi II

Metoda Baade-Wesselink
Hubungan Periode dan Luminositas bintang
Cepheids
Hubungan Periode –Luminositas –Metalisitas
bintang RR Lyrae
4.
Supernova tipe Ia
1.
2.
3.
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In Cepheid's and RR Lyraes, an extra
energy flowing out is held up in the
outer layers for a short while during
the contraction phase and is released
when the star is expanding
This amplifies the contraction or
departure from hydrostatic equilibrium
in the outer layers
Nuclear reactions go at a faster rate
creating more radiative energy and
hence more pressure halting the
contraction.
Perturbation are periodic in most
cases, but some observations show
also long non- pulsating phases.
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Pulsation is not due to variations in the rate of energy
generation in the core but with the variation of the rate of
escaping radiation
Radial pulsations proposed by Arthur Ritter in 1879 assuming
that pulsations are due to sound waves resonating in the
stellar interior.
Use hydrostatic equilibrium, dP/dr = - Gm(r)ρ/r2 = -4Gπrρ2/3
Period~√3π/2Gγρ
This is the period mean
density theorem, where
we take ρ to be the mean
density of the star.
More complicated in
Reality!!
Cepheid’s are much more tenuous
and have a smaller mean density
and hence a longer period. RR
Lyraes are compact with a high
mean density.
The Baade-Wesselink Method
Walter Baade
Adriaan Jan Wesselink
(1893-1960)
(1909-1995)
• Method to get the distances to variable Pulsating stars proposed fisrt by Baade in 1926
and reviewed by Wesselink in 1946
• The Radius:
The Variation of the Radius during one phase of pulsation:
R  R0  R (t )
P
R(t )  q  (Vr (t )  Vr (t ) )dt
0
P
1
 Vr (t )   Vt (t )dt
P0
(a) For a pair of phases with the same
temperature and color (say, B-V), the Cepheid’s
apparent magnitudes V differ due only to the
ratio of stellar radii:
R
m  2.5 lg
R
R1
R2
B-V
2
1
2
2
(b) Radii difference
Pulsation Phase
(R1-R2) can be calculated by integrating the
radial velocity curve, due to VR ~ dR/dt
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A number of pairs
(R1 – R2) ~∫VR·dt and R1/R2 ≈ 10-0.2m
give rise to the calculation of mean radius,
<R> = (Rmax + Rmin)/2
The Baade-Wesselink Method,ct’d
• The Effective temperature:
Using stellar models one gets the effective temperature as a function
of observable color properties and metallicity:


 Fe 
Log Teff  f (V  K ),  , log g 
H 


• The Absolute magnitude:
The Luminosity and absolute magnitude of a black body of a radius R and a
temperature T is given by:
R
L  4 R 2 Te4
M v   2.5 log L  M

Bol
 Fe
 BC (log Teff , 
H

, log g )

And combining with the apparent magnitude, one get the distance
modulus and thus the distance
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The Distance to the Galactic Center was measured via the
BW method d= 7.9 +/- 0.6 Kpc
Distance to the M31: 740+/-40 Kpc
Distance to the LMC: 50+/-2 Kpc
Distance to the NGC6822: 475+/-30 kpc
BW method
Galactic
Centrer (kpc)
M31
(kpc)
LMC
(kpc)
NGC 6822
(kpc)
RR Lyrae
7.8 +/- 0.4
750+/-80
44+/-2
469+/-22
Cepheids
8.0+/- 0.5
760+/-50
50+/-2
477+/-35
other
8.0+/- 0.8
700+/-60
52+/-3
480+/-60
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Among brightest stellar
indicators, relatively young
stars, found in abundance in
spiral galaxies
Many independent objects can
be observed in a single galaxy
Large amplitude & distinct
sawtooth light curve facilitate
discovery
Long lifetimes: can be observed
at other times and wavelengths
P-L relationship has better
precision
Have been studied and
theoretically modeled
extensively and their physics is
understood
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Atmospheric Models (logT,
log g)
Dust scattering, Absorption
and Reddening. Corrections
must be made for extinction
with assumptions
Metallicity: dependence of PL
relationship on chemical
composition very difficult to
quantify (PL relationship has
slight dependence on
metallicity)
Accurate calibration of PL
relation at any given
metallicity not yet established
Limited reach ~30 Mpc
Improvement to the BW technique
using Interferometry
P. Karvella et al 2004
N.Nordetto et al 2005
Lane et al 2002
Lane et al 2000, Nature 407,485
Distance Modulus using the BW method
µNGC1705=28.54±0.26 mag
µM31 = 24.63 ± 0.17 mag
µNGC6822 = 23.36±0.17 mag
µLeoI = 22.04 ± 0.14 mag
µLeoII = 21.83 ± 0.13 mag
µFornax = 20.66 ± 0.10 mag
µDraco = 19.84 ± 0.14 mag
µUMi= 19.41 ± 0.12 mag
µLMC = 18.515 ± 0.085 mag
Clementini et al 2003
(1) Cepheid Variables:
* Period 1 - 100 days
* Named After the first found,
eg. Delta Ceph
* F-type Massive stars M~5Mʘ,
Age ~0.1Gyr
* High Luminosity -6<Mv<-2
(2) RR Lyrae:
* Period 0.5 – 1 day
* O, A type stars, M~ 1Mʘ
* Found in low metallicity systems
* Luminosity L~100Lʘ , Mv~0
(3) W Virginis:
* Old Variable Stars with 1-30 days
* Low mass, low metallicity
* -4.5<Mv<-0.5, called type II Cepheids
(4) Mira Stars:
* Period 80 - 100 days
* Red Variables, most show emission lines
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More Classes:
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Cepheids and RR
Lyrae variable stars
populate Instability
Strip on the HRD
(see blue strip) where
most stars become
unstable with respect
to radial pulsations
Instability Strip
crosses all branches,
from supergiants to
white dwarfs
G.Tammann et al. (A&A V.404, P.423, 2003)
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Instability strip
for galactic
Cepheids
(members of
open clusters
and with BBWB
radii) in more
details:
MV-(B-V) and
MI-(V-I) CMDs
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Young (< 100 Myr) and massive (3-8 MSun) bright
(MV up to -7m) radially pulsating variable stars
with strongly regular brightness change (light
curves)
Typical Periods of the pulsations: from ~1-3 to
~100 days (follow from P ~ (Gρ)-1/2 expression
for free oscillations of the gaseous sphere: mean
mass density of huge supergiants, ρ, is very small
as compared to the Sun)
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Luminosities: from
~100 to 30 000
that of the Sun
Evolution status:
yellow and red
supergiants, fast
evolution to/from
red (super)giants
while crossing the
instability strip
(solid lines)
Evolution tracks for
1-25MSun stars on the HRD
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1907, Henrietta Leavitt (18681921), Harvard Observatory
Astronomer, discovers CV’s
luminosity and period follow
very tight correlation
M = - 2.59 log (P/days) -0.67
Longer period = brighter CV
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The duration of the Cepheids stage is typically
less than 0.5 Myr and, taking also in
consideration the rarity of massive stars at all,
we guess that Cepheids form very poor galactic
population
Statistics of Cepheids discovered:
~3000 proven and suspected in the Galaxy,
~2500 in the LMC,
~1500 in the SMC,
~Thousands are found and, ~50 000 are expected
to populate the Andromeda Galaxy (M31)
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Easily recognized by its high brightness and
periodic magnitude change among other stars,
even in distant galaxies (up to 50 Mpc)
Typical population of young clusters, spiral and
irregular galaxies
Luminosity increases with the Period (P-L
relation)
Cepheids are still among most important
“standard candles”
Cepheid’s in M31
From Bonanos et al. 2003
Large
Magellanic
Cloud
43.2 ±1.8 kpc
47.0 ±2.2 kpc
50.2 ±1.2 kpc
47.5 ±1.8 kpc
Fitzpatrick et al.
(2003)
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Apparent
mean I
magnitude
corrected for
differential
absorption
inside LMC vs
log P(days) for
fundamental
tone (FU) and
first overtone
(FO) cepheids:
<I> ≈ a + b·lg P
PFO / PFU ≈ 0.71
(Δ lg P ≈ 0.15)
W(I)
Brightest Cepheids
Distances are the same:
absolute magnitudes <MI>
are also linear on log P !
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Linearity of log P-log L relation retains also for
Cepheids absolute magnitudes
Simple estimate:
Brightest LMC Cepheids reach <MV> ≈ -7m
These “standard candles” can be seen from the
distance ~50 Mpc (with ~27m limiting magnitude
accessible to HST)
Brightest Cepheids can be widely used as
secondary sources of distance calibrations to
spiral galaxies hosted by SN Ia etc.
We can see Cepheids
even in distant galaxies
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Overtone Cepheids are clearly seen on the
“apparent magnitude – period” diagrams of
nearby galaxies as having smaller periods for
the same brightness
Problem with Milky Way Cepheids: due to
distance differences, how to identify overtone
pulsators among Cepheids with different
distances ?
Milky Way Cepheids sample is supposed to be
contaminated by unidentified first-overtone
pulsators
This problem greatly complicates the
extraction of the P-L relation directly from
observations of Milky Way cepheids
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(a) Trigonometric parallaxes
(HIPPARCOS and HST FGS)
(b) Membership of Cepheids in open
clusters and associations
(c) BBWB mean radii
(d) Luminosity refinement by the
statistical parallax technique
Udalski et al. (1999)
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P-L relation: <M> = a + b·lg P
(a) zero-point
(b) slope
Why not to estimate the slope of
the P-L relation directly from LMC
Cepheids ? –
The slopes of the P-L relations in other
galaxies may differ due to systematic
differences in the metal abundances and
Cepheids ages (A.Sandage & G.Tammann, 2006)
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Before ~2003, most astronomers used the
slope of LMC Cepheids to refine zero-point
of Milky Way Cepheids
If metallicity effects are really important,
application of single P-L relation to other
galaxies populated by Cepheids can introduce
additional systematic errors (see detailed
discussion in A.Sandage et al., 2006)
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Cepheids color excess are uncertain because
of:
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Finite width of the instability strip (~0.2m) due to
evolution effects
Uncertainty of cepheids “normal colors”
Wesenheit index (Wesenheit function) is
often used to reduce the effects of the
interstellar extinction (B.Madore in
“Reddening-independent formulation of the
P-L relation: Wesenheit function”; ROB
No.182, P.153, 1976)
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From true distance
modulus we have:
MV  V  10  5 lg p (mas)  AV
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Wesenheit index
definition:
Constant!
AV
W ( VI )  V  10  5 lg p (mas) 
(V  I )
E( V  I )
Wesenheit index do not depend
on the extincton but only
onSubstituting
the normalapparent
color color
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( V  I )  ( V  I )0  E( V  I )
Normal
color as well as <MV>
we derive:
is linear on lg P
AV
(see
instability
strip
picture!),
W ( VI )  V  10  5 lg p (mas)  AV 
 ( V  I )0 
E( VP  I )
so W(VI) is also linear on lg
AV
 MV 
 ( V  I )0  W ( VI )  MV    ( V  I )0
E( V  I )
where const β = AV/E(V-I) ≈ 2.45±
follows from the extinction law
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Wesenheit Index can be introduced for any
color: W(BV), W(VK) etc.
W incorporates intrinsic color (and Period –
Color relation)
The advantage of using the Wesenheit index
W instead of the absolute magnitude M is
that
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(a) Wesenheit index is almost free of any
assumptions on cepheids individual color excess,
particularly in our Milky Way, and
(b) it reduces the scatter of the P-L relations
F.van Leeuwen et al. “Cepheid parallaxes and the
Hubble constant” (MNRAS V.379, P.723, 2007)
Wesenheit index
W(VI) for 14
Cepheids with most
reliable parallaxes
from HIPPARCOS
and HST FGS:
Route to P-L relation
W(VI)
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W(VI)
W(VI) = α·lg P + γ
days
days
Metallicity differences have been
taken into account empirically, by
adding the term proportional
to
Very poor statistics!
the difference of the galactocentric
distances (due to “mean”
[Fe/H]
Zero-points
Slope
gradient across the galactic disk,
Δ[Fe/H] / ΔRG) ~ -0.05… -0.10 ±
days
days
Multicolor
(BVRCRICIJHK) P-L
relations for galactic
Cepheids
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D.An et al. “The distances to open clusters from mainsequence fitting. IV. Galactic Cepheids, the LMC, and the
local distance scale” (ApJ V.671, P.1640, 2007)
New
distances
New P-L
for the
galactic
Cepheids:
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(c) Distance scale from BBWB radii
Comparing Cepheids P-L derived from 23
cluster Cepheids (red) with that from
Wesselink radii (blue)
(D.Turner & J.Burke, 2002)
Insignificant slop
difference ~0.19
Mean: <MV>≈-1.20m-2.84m·lg P
* Measurement of H0 with the goal of
10% accuracy was designated as one
of the “Key Projects” of the HST
* Using Cepheid variable stars to
measure distances
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M.Marcony & G.Clementini (ApJ V.129, P.2257, 2005)
Periods < 1d
 Examples of
LMC RR Lyrae
light curves in
BV bands
Observations vs
theory
Large amplitude,
Δm ~ 1m
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Examples of the
LMC RR Lyrae light
curves in I band
(OGLE program,
I.Soszynski et al.,
Acta Astr. V.53,
P.93, 2003)
 RR are simply
discernible among
field stars in
stellar systems
 <MV> ≈ +1m
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NIR light curve of RR Lyr star: look at small
amplitude. RR Lyr: nearest star of this type.
Not so bright
as Cepheids
but very
important for
distance scale
subject in the
galactic halos,
bulges and thick
disk populations
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RR Lyrae variable
stars in the
Instability Strip on
the HRD
In contrast to
Cepheids, RR Lyrae
variables are among
oldest stars of our
Milky Way
Evolution status:
horizontal branch
(HB) stars
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RR Lyrae variables populate galactic halos (H)
and thick disks (TD) (as single stars), and
globular clusters of different [Fe/H]
Evolution stage: Helium core burning
Age: ≥ 10 Gyr
LifeTime: ~100 Myr
RR Lyrae
M2
V const ?
BHB
(EHB)
TP
H
TD
Close luminosities for the
same [Fe/H] (rms ~ 0.15m)
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The duration of RR Lyrae stage (and HB stage
at all) is negligible as compared to the age of
stars, ≤100 Myr vs ~10-13 Gyr (<1%), but
comparable with lifetime of Red Giants
Therefore, HB population is comparable with RG
population in size, but RR Lyrae form only a
small fraction of all stars above Turn-Off point
on the CMD
Thousands of RR Lyrae are found and
catalogued in the Milky Way halo and in its
globular clusters
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Dots are separated by
10 Myr time interval
HB position is almost
the same for clusters
of different age
HF
IS
Gyr age
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Universality of RR
Lyrae population
luminosity
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D.VandenBerg et
al. (ApJ V.532,
P.430, 2000)
theoretical
ZAHB levels for
different [Fe/H]
and [α/Fe]
values
[Fe/H] seems to
be the key
parameter
responsible for
RR Lyrae
optical
luminosity
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The slopes of P - L and [Fe/H] - L relations
seems to be definitely found from the
theory as well as from observations in
globular clusters and nearby galaxies differ
by [Fe/H]
Zero-point refinement is Main problem in
RR Lyrae distance scale studies
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From late 1980th, it became customary to assume
a linear relation between RR Lyrae optical
absolute magnitude and metallicity of the form
<Mopt> = a + b·[Fe/H]
The calibration problem reduced to finding a and
b by whatever calibration method was used. The
three most popular have been:
(a) theory
(b) the BBWB moving atmosphere method
(c) distances of globular clusters; HST &
HIPPARCOS parallaxes
(d) statistical parallaxe technique
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Is there universal slop of the <MV> - [Fe/H]
relation?
Theoretical
slopes μ
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RR Lyrae models in NIR do obey to a well-defined
PLZK relation:
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<MK> ≈ -0.775 − 2.07·lg P + 0.167·[Fe/H]
with an intrinsic scatter of ~0.04m
(with small contribution from [Fe/H] term)
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<MI> ≈
<MJ> ≈
<MH> ≈
<MK> ≈
+0.109 – 1.132·lg P + 0.205·[Fe/H]
-0.476 – 1.773·lg P + 0.190·[Fe/H]
-0.865 – 2.313·lg P + 0.178·[Fe/H]
-0.906 – 2.353·lg P + 0.175·[Fe/H]
<MV> ≈ +1.258 + 0.578·[Fe/H] + 0.108·[Fe/H]2
(this nonlinear function of [Fe/H] do not depend
on lg P:
<MV> ≈ +0.63m at [Fe/H]=-1.5 )
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Usually, RR Lyrae distance scales are
characterized by the mean absolute
magnitude referred to [Fe/H] = -1.5, the
maximum of [Fe/H] distribution function of
RR Lyrae field stars and GGC (galactic
globular clusters)
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Cepheids as very bright and uniquely identified
stars are among most “popular” standard candles
in the distant galaxies, but their distance scale is
still uncertain by ~10% (systematic + random
error)
RR Lyrae are good standard candles used to refine
the distances to the “beacon” galaxies (such as
LMC/SMC, M31/33 etc.) in the Local Volume (up
to ~10 Mpc), and to calibrate other secondary
standard candles (SN Ia, Tulli-Fisher & FaberJackson relations etc.)
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Much work has to be done with Cepheids and
RR Lyrae variables in recent years and in the
future, in the context of GAIA and SIM
observatories
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SNe advantage: extremely bright (as bright
as whole the galaxy !) and easily
discriminated (if you are lucky enough to
detect it early)
Seen in high-z galaxies, SNe can reveal early
Universe’s kinematics and provide the check
of the cosmological models
Give rise to completely new physics of late
stages of stellar evolution
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Supernovae explosion events are very rare and
spectacular phenomena on the heavens
Last two SNe in our Milky Way Galaxy:
SN 1572 (Tycho Brage’s supernova Ia (?) in the
Cassiopeia constellation) achieved -4m at the
maximun brightness
SN 1604 (Kepler’s supernova Ia in the
Ophiuchus constellation) achieved -2.5m
As expected, we could have miss a number of
Supernovae events that have been exploded
deep inside the galactic disc full of dense and
opaque interstellar dust
Bright SN1994D (Ia)
SN1994D
Milky Way-like galaxy
A supernova can outshine an entire galaxy,
and so be seen from very far away
Why not to use for distance measurement ?
Core collapse of a massive star:
Type II Supernova
If an accreting White Dwarf exceeds the
Chandrasekhar mass limit, it collapses,
triggering a Type Ia Supernova.
Type I: No hydrogen lines in the spectrum
Type II: Hydrogen lines in the spectrum
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Type I
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Subgroups are Ia (no H, no He), Ib/c (no
H), outer stellar layers are already missing
prior to the explosion – due to binary
system evolution ?)
Found in elliptical, spiral and irregular
galaxies as well (Ia) or only in star-forming
galaxies (I b/c – young population ?)
Type II
Hydrogen is observed in spectra
 Probably originated from high-mass stars
 Found only in star-forming galaxies
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SN1987A
How to classify Supernovae?
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Type Ia – thermonuclear supernovae exploded
in close binaries with companion white dwarf,
which exceeds ~1.4 MSun Chandrasekhar limit as
a result of the mass exchange
Type Ib/c and II – core-collapse supernovae,
final stages of the evolution of (very) massive
stars that ends up as NS or BH
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(a) Single stars that are typically below ~8
MSun becomes red giant just after their life
on the Main Sequence
Red giants lose mass and evolve (often
through a Planetary Nebulae stage) into
White Dwarfs
(b) More massive stars become supergiants
Supergiants undergo Type II (and extremely
massive – Type Ib/c) Supernova explosions,
often leaving behind a stellar core which is a
neutron star (NS), or a black hole (BH)
Sun-like stars build up a
Carbon-Oxygen (C-O)
core, which does not
ignite Carbon fusion
With He-burning shell,
stellar C-O core collapses
and becomes degenerate
White Dwarf
The more massive a White Dwarf, the denser and smaller it is
Pressure becomes larger, until – at the mass limit - electron
degeneracy pressure can no longer hold up against gravity.
WDs with more than ~ 1.4 solar
masses can not exist!
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SN Ia event is due to mass transfer
in close binary system with White
Dwarf as a satellite of normal star,
filling its Roche surface, through
inner Lagrangian L1 point
When the White Dwarf reaches the
“Chandresekhar limit” of ~1.4 MSun, it
implodes with a bright flash of
energy released due to Carbon and
Oxygen thermonuclear fusion inside
the star
In a binary system, each star controls a finite region of space,
bounded by the Roche Lobes (or Roche surfaces)
Lagrange points: points of
stability, matter can rest
(with zero velocity) without
being pulled towards one of
the stars
Gas can flow over from one star to another through the inner
Lagrange point, L1
(a) More massive star B evolves
more quickly, it becomes a red
giant and loses mass through L1
point; after a while it becomes the
White Dwarf star
(b) Main Sequence star A gains the
mass and becomes more massive;
after a while it loses its mass to
WD satellite
Mass transfer in a close binary system
can significantly alter stellar masses and
affect their evolution
This process in more details
Start
Nothing remains after WD explosion…
Companion star ejecting
End
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Fixed limiting mass of the White Dwarf
(~1.4 solar) together with known physical
description of thermonuclear reactions of
Carbon & Oxygen nuclear burning, suggest
the similarity of SN Ia properties used to
derive the distances to SNe host galaxies
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SN Ia : ~45%, explodes in spiral, irregular
and elliptical galaxies
SN II + SN Ib/c : ~55%, explodes only in
spiral and irregular (star-forming ) galaxies,
and most luminous (SN Ib/c) – in the regions
of current star formation populated with
youngest massive stars
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NGC 6946 (~3·1010 LSun) is the champion, with its
6 SN (!) registered from 1917
SN rate for Milky Way is supposed to be ~1
SN/100 years, but the last observed SN
exploded in 1604 - selection effects due to
strong interstellar extinction or not ?
NGC 2770 with
its two SN (2008)
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Supernova taxonomy
SN Ia spectral features
α-elements:
20Ne 24Mg 28Si 32S
40Ca…
Primary nuclides,
formed from He
A.Filippenko “Optical spectra of Supernovae”
(ARA&A V.35, P.309, 1997)
 Comparison
of Ia, II, Ic,
Ib spectra
after 1 week
from maximum
Ia & Ic: no H,
no He
 Deeper lines
in SN Ia
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Ia
II
Ic
Ib

A.Filippenko (1997): expansion velocity for
SN Ia vs time (from spectral data)
> 10000 km/s
Total kinetic
energy output
~ 1051 ergs
(a) To explain SN Ia events among both old and
young populations
 (b) To explain the absence of Hydrogen in their
spectra
 (c) To explain widely accepted idea of the
homogeneity of the SN Ia class
-------------------------------------------------Accretion rate is key parameter: small rate !

Qualitative SN Ia light curve
56Ni
+ 56Co  56Fe decay rate
Early decay heating explains the
luminosity rise
1043
Optical light curve
.
1042
0
20
40
t (days after peak)
Decay produces
gamma-rays
60

A.Hirschmann et al. (2007) for different
detonation models: a lot of radioactive 56Ni


C.Travaglio et al. “Nucleosynthesis in multidimensional SN Ia explosions” (A&A V.425,
P.1029, 2004):
Element yields (mass-to-Fe fraction/the same
for Sun); Fe = 1. Ni in excess !
The results from two different models
From
C.Travaglio et
al. (2004)
 Stable isotopes
masses in MSun
Most abundant are underlined


C, O, Mg, Si, S, Ca, Cr, Mn, Fe, Ni are
most abundant elements
 We
all and all things
around us have borne in
Supernovae explosions !


Real physical picture of the SN Ia ignition is
very complex, with non-trivial topology of the
ignition fronts, explaining the differences
between models proposed. But a number of
numerical simulations in 3D have been
performed in the last decade
Two main models of the burning front spread
(from C.Travaglio et al., 2004):
Central ignition
 Floating Bubble model (with a small number of
primary ignition centers)

Central ignition front snapshots after
T = 0, 0.2,
1
0.4 and 0.6 s

3
2
4
Floating bubbles front snapshots after
1
T = 0, 0.1,
0.14 and 0.2s

3
2
4
 The
adequate physical model
of the SN Ia explosion is
yet to be created


Individual Supernovae light-curves differ in peak
luminosity by the factor of about 6-10
How can we use SN Ia as the “standard
candles”?



(a) Correct photometric data for interstellar
extinction in host galaxy and inside the Milky
Way
(b) For high-z SNe, calculate K-correction
due to redshift of the energy distribution
(c) Calculate “stretching” factor and fit SN
Ia light curve by the template


Some SN Ia explode in galactic halos and often
are not greatly affected by the extinction in
host galaxies, whereas most SN Ia infound in
Riess et al., 1998
star-forming galaxies are embedded into dusty
spiral arms
Except for a small group of very rapidly fading
supernovae (fainter), at maximum light, SNe Ia
are supposed to have a relatively small scatter in
their intrinsic colors, Δ(B-V)Max ~ 0.2, near <BV>Max≈0.05m, that depend on the rate of lightcurve decline and is used to crudely estimate the
extinction



Energy redistribution to larger wavelength in
the spectra of high-z SNe is adjusted by
calculations of K-corrections to the apparent
magnitude in ith band:
mi (z) = mi (z=0) + Ki (z), where
Si(λ) is ith bandpass curve, and (1+z)=λ/λ0
accounts for the shift to red and of the
increase of Δλ wavelength interval
z effect to
passbands
(shifting and
stretching)
z=0.2
z=0.5


SNe energy distribution shifts to the red, as if
filter passband was shifted to the blue (in rest λ)
R passband shift for z = 0.2, 0.5 is shown, as
compared to standard Johnson B & V color bands:
R(z = 0.2) is bluer than V, R(z = 0.5) looks like B !





Supernovae light curves differ from each other
by the (a) rate of the brightness decline, (b)
the peak luminosity and (c) color at maximum
light
The diversity of their light curves can be fitted
by single light curve “template” that can be
“stretched” by time axis and shifted by
magnitude axis
M.Philips relation (ApJ V.413, L105, 1993):
Dimmer SN Ia – faster brightness decline
Dimmer SN Ia – redder color at maximum light

Philips relation (maximum
brightness vs rate of the decline)
is continuously adjusted by new
data on SN Ia, derived from
multicolor observations



K.Krisciunas et al.
(AJ V.125, P.166,
2003)
SN 2001el in NGC
1448 host galaxy
(~18 kpc)
One of the best
studied SN Ia in
multicolor
(UBVRIJHK), from
12d before to 142d
after maximum, to
check the theory


K.Krisciunas et al.
(2003)
Optical and NIR
light curves of SN
In JHK, maximum
earlier
than in
2001el
(shifted
optics
vertically)
-6
-5
-4
-2
B-V
-1
Max
+1
+2


SN Ia bolometric light curve: ~2·1043 erg/s of
radiative energy flux near maximum light
Total energy output > 1051 ergs
SN 1998bu



A.Riess et al (AJ
V.116, P.1009,
1998):
Empirical SN Ia
light curves
Δ=MMax-<M> is the
magnitude
difference at the
maximum light
between SN Ia
and the “fiducial”
light curve
(template)
Data for 2 SN Ia are shown



A.Riess et al. (AJ
V.607, P.665, 2004)
SNe with z > 1 from
HST as compared to
low-z SN Ia:
composite light
curves
Low-z and high-z SN
Ia seem to be similar
in the light-curve
shapes: the same
explosion physics ?



All SN Ia are not the
same!
Correlations: slowbright, blue-bright
Manage us to use
light-curve
“templates” and
different templatefitting techniques
Peak
brightness
Colour
Index (CI)
Light curve
width (stretch)
B  mB  MB   ( s  1)    CI
Corrected distance modulus

Corrected absolute magnitude of the observed
SN Ia as:
MFit = MT - α·(s-1) + β·ΔCI,
where stretch factor (light curve “width”) s =
Δm15T /Δm15, CI - Color Index,
ΔCI = CI - CIT, (“T” for template curve)
Δm15 – magnitude decay after 15 days (the
faster is SNe, the more magnitude decay)
(a) For slower SN, s > 1, MFit < MT, SN brighter
and distance modulus larger
(b) For redder SN, ΔCI > 0, MFit > MT, SN
dimmer and distance modulus lower


Why expect β~4 ? Color problem:
RB = AB/E(B-V) =AV+1,
β factor at CI is due to so RB ≈ 4.1 for “mean”





extinction law in MW
Extinction inside host galaxy and Milky Way
Intrinsic properties of SN Ia (colors)
β (at B-V color) from SN observations ~2
instead of ~4 we could expect from “standard”
extinction curve in the MW
SN Ia
distances,
RB To~ be2sure
is in
not
seen
anywhere in the MW!
we have to solve the problem
The reasons: “Strange” dust changed by the SN
explosion? Dust evolution with z? Cannot
discriminate an intrinsic Color-Luminosity
relation from extinction?




Advanced light curve fitting methods:
(a) MLCS (Multicolor Light-Curve Shape) –
A.Riess et al. (PhD Thesis, Harvard University,
1996; ApJ V.116, P.1009, 1998)
(b) CMAGIC (Color-MAGnitude Intercept
Calibration) – L.Wang et al. (ApJ V.590, P.944,
2003) – enables to estimate extinction as well
(c) SALT (Spectral Adaptive Light-curve
Template) – J.Guy et al. (A&A V.443, P.781,
2005)


K.Krisciunas et al. (2006)
In NIR, SN Ia are
more alike to the
“standard candles” –
max (JHK) are nearly
constant (except for
fastest SN), with
rms scatter ~0.14m,
distance error ~7%
from individual SN
Seems to be very
perspective



Are SN Ia really “standard candles”?
Some people doubt in homogeneity of
supernovae SN Ia sample and even consider SN
II type as possible “standard candles”
candidate
More extensive calculations of SN explosions
are needed and new rich SN statistics, with
spectral and multicolor photometric data, to
answer all questions


D.Branch & G.Tammann (1992) emphasized the
observational homogenity of SN Ia:
The intrinsic dispersion in absolute magnitudes,
MB and MV, after correction for extinction by
intervening interstellar dust in our Galaxy and
the supernova parent galaxies, was estimated to
be no more than 0.25m, which corresponds to a
dispersion of only 13% in distance when SN Ia
are used as standard candles. This luminosity
homogeneity, together with the extremely high
luminosity of SN Ia (~1010 LSun) that makes them
detectable across the universe, make SN Ia
extremely attractive as distance indicators for
cosmology

As distance indicators SNe Ia are invaluable.
They provided the first evidence of an
acceleration of the cosmic expansion and are
currently the best objects to determine the
dynamics of the universe. However, we need to
understand these explosions better to raise
confidence in the claims. The normalisations
applied so far are entirely empirical and the
different methods in use are not consistent
with each other. Also, as long as we have the
uncertainties on progenitor system, explosion
mechanism and radiation transport, which
ultimately provide the observable light,
questions remain about the distances derived
from supernovae beyond a redshift of about
0.2
SN Ia luminosity can depend on the
metallicity (age) of early-type galaxy
(J.Gallagher et al., ApJ V.685, P.752, 2008):
from
29 galaxies SNe

Dimmer in
more metalrich (perhaps
older) galaxies
ΔM

From J.Tonry et al. (ApJ V.594, P.1, 2003)
Estimated
apparent
magnitudes
at the
maximum
light for
high-z SN
Ia
Extrapolated
in ()
Accessible to observations
with large telescopes




G.Altavilla et al. “Cepheid calibration of Type Ia
supernovae and the Hubble constant” (MNRAS
V.349, P.1344, 2004)
Cepheid distances to 9 SN Ia host galaxies
Cepheids P-L relation was used, consistent with
LMC distance ~50 kpc (m-M)0≈18.50m, in
agreement with the HST Key Project
Distances to 96 SN Ia have been calculated and
local Hubble constant estimated as 68-74
km/s/Mpc



G.Altavilla et al. (2004)
List of SN Ia and Cepheid host galaxies (only
9!) used to calibrate SN Ia luminosities
SN Ia zero-point under different assumptions
lies in the range MB ≈ -19.60…-19.40m




C.Ngeow & S.Kanbur “The Hubble Constant from
Type Ia Supernova Calibrated with the Linear
and Non-Linear Cepheid Period-Luminosity
Relations” (ApJ V.642, P.29, 2006)
Cepheid distances to 4 SN Ia host galaxies with
142 Cepheids in total
Cepheid P-L (linear and nonlinear) have been
used based on LMC Cepheids, with LMC distance
also as (m-M)0≈18.50m
Galaxies distances ~16 Mpc
 Supernovae
for
cosmology: state of art
 Estimating
ΩM, ΩΛ and w
(equation of state parameter)
 (ΩM
= ΩB + ΩDM)



(a) SN Ia Magnitude describes the expansion of
light sphere with respect to comoving
coordinates
(b) SN Ia Redshift reflects the expansion of
comoving coordinates
Comparison of the apparent distance modulus
with RedShift (z) can set the limits to the
cosmological model and constants involved
Hubble diagram
for different
pairs (ΩM,ΩΛ)
Best-fit flat solution:
(ΩM, ΩΛ) ≈ (0.28, 0.72)
0
0.2
0.4
0.6
0.8
1.0 z



For the first time cosmological constant Λ have
been estimated at high confidence level, giving
rise to Dark Energy (or vacuum energy) with its
unique property of universal repulsion (or
antigravitation), in contrast to gravitational
attraction known before
Dark Energy became newest field of interest
for cosmologists and cosmo-micro-physicists
Now it turned clear that baryonic matter
(ordinary matter) make only 4-5% of all energy
density in the Universe, whereas Dark Energy
greatly dominates
Best-fit
confidence
regions
(68%, 90%)
 Note that lines
of constant
Universe age
are nearly
parallel to
contour lines:
Age ~ 14.9 Gyr
(for flat model)

and the fate of the Universe
Our future depends on how
the Universe has expanded
in the past
SELESAI