nikolai kolachevsky lecture 6 - power1.pc.uec.ac.jp
TRANSCRIPT
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Lecture 6
• Pulsars as astrophysical sources of periodic pulses.
Physics of pulsars.
• Drift of periastrium and General relativity tests.
Radiation of gravitational waves.
• Quasar spectra. Search for drift of the fine structure
constant.
• Calibration of astrophysical spectrometers. Search for
exasolar planets.
Nikolai Kolachevsky
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Pulsars – precise natural clocks in the Universe
Shortest observed pulse period 1.3ms
Angular velocity: Mass:
Highest density – neutron star density
Speed on the surface < c!
=> Rmax=50 km
Rotation period ~ 1 ms – seems to be true!
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Neutron stars and white dwarfs
Neutron star – neutron-
proton Fermi liquidElectron-degenerate
matter
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Equations of state a white dwarf
Electron-degenerate
matter (electron-nuclei plasma)= 105 – 109 g/cm3
Non-relativistic case
High-energy electron move
very fast
Relativistic regime!
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Equations of state a white dwarf
Relativistic case
Pressure:
Gradient:
Electron gas pressure Gravity
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Chandrasekar limit
1.44 solar mass !
If mass becomes higher -> supernova class Ia
Standard candle
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Hubble constant determination
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Emission pattern
Pulsar’s “fingerprints”Slow pulsars
Millisecond
pulsars
Period variation
Millisecond pulsars are old (billion years),
rather weak magnetic field
Have orbital twins!
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Pulsars: magnetic field increases!
Initial star (Solar radius)
Pulsar
Magnetic flow is conserved
Magnetic field can reach
Or even higher
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Deceleration due to electromagnetic radiation emission
Rotating magnetic dipole
Energy taken from rotation
Huge inertia moment
Energy dissipation Comparable to the Sun radiation
One can evaluate magnetic
moment
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Pulsar chronometry
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Binary star system (binary pulsars)
Hulse and Taylor -> Nobel Prize 1993
The period of the orbital motion is 7.75 hours,
and the stars are believed to be nearly equal
in mass, about 1.4 solar masses.
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Arrival time variation
When the pulsar is on the side of its orbit closest to the Earth, the pulses
arrive more than 3 seconds earlier that they do when it is on the side
furthest from the Earth. The difference is caused by the shorter distance
from Earth to the pulsar when it is on the the close side of its orbit. The
difference of 3 light seconds implies that the orbit is about 1 million
kilometers across.
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Period variation
Velocity of the pulsar changes as it
moves through its orbit. When the pulsar
is moving towards us and is close to its
periastron, the pulses should come
closer together.
Gravitational field is stronger => the
pasage of time is slowed down
The time between pulses (ticks)
lengthens just as Einstein predicted.
The pulsar clock is slowed down when
it is travelling fastest and in the
strongest part of the gravitational field
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The observed advance for PSR 1913+16 is
about 4.2 degrees per year; the pulsar's
periastron advances in a single day by the
same amount as Mercury's perihelion
advances in a century.
Rotation of periastron
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Gravitational waves emission?
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Power radiated by Gravitational waves emission?
Earth-Sun system
200 W power in gravitational waves
Wave amplitude
For the distance of 1 light year
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Search for the possible variation of
the fine structure constant
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Schrödinger: Schrödinger in atomic units:
Use atomic units no adjustable parameters !
Adjust parameter to match observations.
Dirac in atomic units: Full recoil and QED:
Fundamental Constants in Quantum Mechanics
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Parameters express our ignorance.The standard model has 18 of them.
The Role of Parameters
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What‘s the Problem with the
Fundamental Constants ?
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Fundamental Constants
- Why do the constants have the observed values?- Can‘t be calculated standard model is incomplete.- Look for phenomena beyond the standard model.- A complete theory should produce small numbers.
Dirac 1937: The age of the universe in atomic units divided by the electromagnetic force between an electron and a proton
measured in units of their gravitational force is such a small number (believed to be 3 in 1937).
Almost every „constant“ could vary in time.
small numbers
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Evolution of the Universe
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Search for Drift
t1t 2t
1( )t 2( )t - stable value
(dimensionless)
e.g.
cross-section ratio,
mass ratio,
frequency ratio, ...
1 2( , ,...) depends on a set of
fundamental parameters
2 1
2 1
( ) ( )t t
t t
i
t
Model
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Search for Drift
t1t 2t
1( )t 2( )t - stable value
(dimensionless)
e.g.
cross-section ratio,
mass ratio,
frequency ratio, ...
1 2( , ,...) depends on a set of
D.Hanneke et al., PRL 100, 120801 (2008)
the value of is known to 410-10 (40 years => )11 110 yr
Sensitivity to the DRIFT is much higher!1710
fundamental parameters
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Sensitivity to variationsfor different methods
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Oklo Phenomenon
Natural fission 235U/238U reactor
2109 years ago
resonance by 0.1 eV
A.I. Shlyakhter, Nature (London), 264, 340 (1976)
149 150
62 62Sm Smn
Abundance ratio:
149 147
62 62Sm Sm(typical)
(Oklo)0.02
0.9
8( 0.36 1.44) 10
Y.Fujii et al., Nucl. Phys. B, 573, 377 (2000)
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Atomic Spectra
1/ 2S
1/ 2P
3/ 2PFS
optical
Transition Scaling
Optical
Fine structure
Hyperfine
structure
Ry
2Ry
2
nucl B Ry
1emission
today
z
FS
optical~ 2
M.P. Savedoff, Nature, 178, 689 (1956)
HFS
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Quasar Absorption Spectra
J.K. Webb et al., Phys. Rev. Lett. 87, 091301 (2001)
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"Many-Multiplet" Method
( )NR relf f F Z
depends only on
e
Z( )relF Z
1
2
(1)lnln ln
ln (2)
rel
rel
Ff
t f t F
measurable
valueto be
determinedcalculated from
basic principles
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Keck/HIRES results
5( 0.57 0.1) 10
J.K. Webb et al., Phys. Rev. Lett. 87, 091301 (2001)
15 10.5 10 yr
time [109
year]
[1
0-5
]
Keck / HIRES (72 systems):
MgI, FeI, NiI, MgII, CrII, etc.
-1,5
-1,0
-0,5
0,0
0,5
-2 -4 -6 -8 -10 -12
- many-multiplet
- H I H/ 2
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Recent astrophysical results
• Murphy et al, 2003: Keck telescope, 143 systems,
23 lines, 0.2<z<4.2
/0.543(0.116) x 105
• Quast et al, 2004: VLT telescope, 1 system, Fe II,
6 lines, z=1.15
/0.4(1.9)(2.7) x 106
• Srianand et al, 2004: VLT telescope, 23 systems,
12 lines, Fe II, Mg I, Si II, Al II, 0.4<z<2.3
/0.6(0.6) x 106
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Comparison of sensitivities
Big Bang
13.8 yrG
t
( )Oklo
810 ~
(many-multiplet)
610 ~
1010 yrT ~
1610 <
10 yrT ~
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Optical Frequency Metrology
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high sensitivity to drift (< 1016)
short time intervals (~10 yrs)
high reproducibility, big variety of samples
straightforward analysis of systematics
weak model dependence
Laboratory experiments
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Ellipse Plot
T. Rosenband et al. SCIENCE 319, 1808 (2008)
16 1( 1.9 4.0) 10 yr
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1016
1015
1017
year
H, Hg , Yb+ +
Keck/HIRES
VLT
VLT
H, Hg , Yb+ +
Hg+ и Al
+
2002 2004 2006 2008sen
sitiv
ity t
o
[1
0 y
r]
/
-15
-1
Sensitivity to linear drift
Astro
Lab
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Laser Frequency Combs for Astronomical Observations
Image: ESO T. Steinmetz et al, SCIENCE 321, 5894 (2008)