1. Chapter 4- Timing PHY6795O – Chapitres Choisis en Astrophysique
Naines Brunes et Exoplanètes
Chapter 4- Timing
PHY6795O - Naines Brunes et Exoplanètes

2. PHY6795O – Naines brunes et Exoplanètes
Contents
4.0 Introduction
4.1 Pulsars
4.2 Pulsating stars
4.2.1 White dwarfs
4.2.2 Hot subdwarfs
4.3 Eclipsing binaries
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4. Timing

3. PHY6795O – Naines brunes et Exoplanètes
4.0 Introduction (1)
Principle
The motion of planets in orbit around a star causes the star to undergo a reflex motion around the barycenter which can be measured either through a change in the radial velocity of the star or a change in its position in the sky (astrometry).
The reflex motion of the star can also be inferred if the star features a periodic signal that will vary due to the Doppler effect.
Three types of periodic signal
Radio pulsars
Pulsating stars (white dwarfs, subdwarfs)
Eclipsing binaries
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4. Timing

4. PHY6795O – Naines brunes et Exoplanètes
4.0 Introduction (2)
The timing method refers to the timing delay τp associated with the light travel time associated with the reflex motion of the star around the barycenter, defined as
For a circular orbit, the amplitude of the time delay is
observer
Orbital plane
(4.1)
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4. Timing

5. 4.0 Introduction (3) Discovery status (end of 2010)
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4. Timing

6. 4.0 Introduction (3) Discovery status (past 2010; not complete)
PHY6795O – Naines brunes et Exoplanètes
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7. PHY6795O – Naines brunes et Exoplanètes
Contents
4.0 Introduction
4.1 Pulsars
4.2 Pulsating stars
4.2.1 White dwarfs
4.2.2 Hot subdwarfs
4.3 Eclipsing binaries
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4. Timing

8. PHY6795O – Naines brunes et Exoplanètes
4.1 Pulsars (1)
Rapidly rotating highly-magnetized neutron stars with magnetic axis beamed towards the Earth
Violent formation through core collapse of massive (~8-40 M) stars in a supernova explosion.
Emit two narrow beams of radio emissions aligned with magnetic axis.
Two classses:
Normal pulsars with P~1s
msec pulsars, i.e., ‘recycled’ old neutron stars
spun-up to vey short periods during mass and
angular momentum transfer from a binary
companion. Most msec pulsars still have
binary companions, either white dwarfs or
neutron stars.
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9. PHY6795O – Naines brunes et Exoplanètes
4.1 Pulsars (2)
msec pulsars are extremely accurate clocks
Periods changing through tiny spin-down rate (10-19 ss-1).
Pulse arrival time residuals measured with μs accuracy.
Known pulsar population: 1700
80 msec pulsar in the Galaxy
130 in Galactic globular clusters
11 with distance less than 300 pc
For a circular edge-on orbit of period P, and assuming a canonimal neutron star mass of 1.34 M,
Possible to detect moon-size planets with μs accuracy.
Ex: Mp~0.01 M, P~30 days, τp~2 μs
(4.2)
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10. 4.1 Pulsars (3) Factors affecting the timimg delay
The general formulation of the barycentric pulse arrival time, tB, is (Wolszczan & Kuchner 2011; Eqn 11)
tclk : clock correction that accounts for differences between the observatory clocks and terrestrial time standards.
r : net vector of the observatory to the barycenter. Sum of three vectors pojnting Earth’s center, from there to the center of the Sun, and then to the source.
n: unit vector in the direction of the pulsar.
with the ecliptic latitude. This is the Roemer delay, the travel time within the Solar system. This is the most uncertain correction since it requires a very accurate knowledge of the pulsar’s sky position.
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4. Timing

11. 4.1 Pulsars (4) Factors affecting the timimg delay
D’ : a constant related to the column density of interstellar electrons along the line of sight.
f : the frequency of the observations.
: ‘Shapiro’s delay’ acquired by light propagating through curved space,
is the pulsar-Sun-Earth angle computed from the solar system ephemeris.
~120 μs for the Sun, ~200 ns for Jupiter
: Einstein’s delay. The combined effect of time dilation and gravitational redshift of the signal due to the annual variation of a terrestrial atomic clock as Earth moves around the Sun on its eccentric orbits and to the presence of other masses in the solar system. Maximum correction of this term is ~1.66 ms.
tR : additional Roemer delay due to the Keplerian orbital motion of the planet.
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12. PHY6795O – Naines brunes et Exoplanètes
4.1 Pulsars (5)
PSR B
First exoplanets ever found (Wolszczan & Frail 1992)
Distance: d~300 pc
Initially discovered as a two planet system
M sin i = 2.8 and 3.4 ME, a=0.47 and 0.36 AU.
Orbital periods (98.22 and d) close to a 3:2 resonnance
Long term monitoring show evidence of planet-planet interaction (see next slide)
Enable mass estimate without a priori knowledge of the inclination
Provide evidence for a third close-in planet: P=25.34 d, Mp=0.02 ME
One the smallest planet ever discovered.
Dynamical studies suggest the system to be stable over a timescale
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13. 4.1 Pulsars (6) PSR B1257+12 – Planet-planet interaction
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14. 4.1 Pulsars (7) PSR B1257+12- Formation mechanisms
Planet formed around a normal (massive) star, the pulsar progenitor. Its present existence implying that it must have survived the supernova explosion.
Planet formed around another star before being captured by the pulsar through dynamical interaction.
‘’Fallback accretion’’. Planet formed after the supernova explosion which created the neutron star.
Supernova need to retain some residual material that could fall back to form a debris disk around the young neutron star.
Difficulties in modelling planets which survive the supernova explosion may favour the ‘fallback’ accretion disk model.
Fallback model imply the existence of a dust disk.
Attempt to detect it by SPITZER failed so far.
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15. PHY6795O – Naines brunes et Exoplanètes
4.1 Pulsars (8)
PSR B
11-ms pulsar discovered in globular cluster M4.
Has a binary companion, a 0.3 M white dwarf in a 191-d low eccentricity orbit.
10 MJ planet orbiting pulsar-WD binary with a~35 AU, P~100 yr.
Such a wide companion can survive the dense environment of the cluster (Woolson 2004).
Signatures of Newtonian interactionb between planet and WD observed.
Formation scenarios
Planet forms around a main sequence star, then
Migration towards the cluster core where it encounters a neutron star binary.
One neutron star captures the star and planet, and ejects its original neutron star companion.
The main sequence star evolves into a red giant (and eventually a WD), transfering mass and so spinning up the neutron star to its final ms pulsar status.
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16. 4.1 Pulsars (9) PSR B1620-26 – Fomation mechanisms
2. Planetary system encounters a pre-existing binary millisecond pulsar or a pulsar/WD binary.
Planetary system is disrupted, with the main sequence star being ejected and the planet captured.
Both scenarios require the formation of a planetary system is a low-metallicity globular cluster environment, which appears to occur with low probability. Hence a third scenario,
Planet formed through gravitational instability through a passing star perturbing the common-envelope of a main sequence/giant binary.
Most massive component becomes a supernova
Main sequence star then transfers mass, spining up the neutron star to its msec pulsar status befie evolving to a white dwarf.
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17. 4.1 Pulsars (10) Pulsar planetary formation mechanisms
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18. 4.1 Pulsars (10)
Pulsar planetary formation through gravitational instability
Beer et al. (2004)
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19. PHY6795O – Naines brunes et Exoplanètes
Contents
4.0 Introduction
4.1 Pulsars
4.2 Pulsating stars
4.2.1 White dwarfs
4.2.2 Hot subdwarfs
4.3 Eclipsing binaries
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20. PHY6795O – Naines brunes et Exoplanètes
4.2 Pulsating stars
Scientific interests of probing evolved stars for planetary systems
Provides insight into the future of the solar system in general and Earth in particular.
In survivability is robust, detecting such planets is another route to characterizing their frequency and distribution.
4.2.1 White dwarfs
End point of most stars up to ~8 M.
Common in the solar neighborhood.
Planetary system survical to red giant phase depends on several parameters:
Initial orbit separation.
Stellar mass-loss rate
Tidal forces
Details of dynamical interaction with ejected material.
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4. Timing

21. 4.2.1 Pulsating stars – white dwarfs
Fate of planetary systems during the red giant phase.
All planets within the final extent of the red giant envelope will be engulfed and migrate inwards.
Planets further out will have greater chance of survival, migrating outwards as mass is lost from central star.
In mass is loss instantaneously, planet could escape the system.
Planetary orbits should expand adiabatically (constant energy)
Ex: for a 1 M projenitor evolving into a 0.5 M white dwarf leads to orbits expanding by a factor of two.
In the process, some stable orbits might become unstable.
Orbits with initial a > 0.7 AU remains larger than the primary star radius at all stages of its evolution.
WD could potentially host surviving planets with P > 2.4 yr.
Two observing approachs for finding planets around WD:
Pulsation timing
Direct imaging (later)
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22. 4.2.1 Pulsating stars – white dwarfs
Pulsating white dwarf
As WD cools through certain temperature ranges,
C/O (~ 105 K; GW Vir), He (2.5x104 K; DBV) and H (104 K; DAV) in its photospheres progressively become partially ionized, driving multi-periodic non-radial
g-mode (gravity driven) pulsations.
Pulsation periods: s.
Include some of the most stable know, both in amplitude and phase.
Ideal targets for the timing method.
e.g., G117-B15A
(4.3)
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23. 4.2.1 Pulsating stars – white dwarfs
Pulsating white dwarf
A planet with an orbital period much longer than the observational baseline gives rise to an apparently linear change in pulsation period,
where P is the white dwarf pulsation period.
Ex: Mp=1 MJ, a=10 AU, P=100 s,
Three possibilities for period variation not associated with a planet.
Inherent to the white dwarf cooling:
Known wide-separation proper motion companion not necessarily gravitationally bound
Proper motion. Important for nearby system (Pajdosz 1995)
(4.4)
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24. 4.2.1 Pulsating stars – white dwarfs
Pulsating white dwarf
GD 66 b, best candidate planet aound a WD.
Monitoring since 2003 (2.1, McDonald Observatory)
Variations consistent with a ~2 MJ in a 4.5 yr orbit
Under the list of ‘unconfirmed’ planets in
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25. 4.2.2 Pulsating stars – hot subdwarfs
Hot subdwarfs, of spectral types O and B, also termed "extreme horizontal-branch stars, represent a late stage in the evolution of solar-mass stars caused when a red giant star loses its outer hydrogen layers before the core begins to fuse helium.
Like WD, some subdwarfs are pulsating
Première découverte: V391 Peg b (Silvotti et al, 2007)
Découvertes récentes par la mission Kepler
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26. 4.2.2 Pulsating stars – hot subdwarfs
V391 Peg b
Progenitor mass: ~1 M
Planet properties: Mp sin i = 3.2 MJ, a=1.7 AU and P=3.2 yr
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27. PHY6795O – Naines brunes et Exoplanètes
Contents
4.0 Introduction
4.1 Pulsars
4.2 Pulsating stars
4.2.1 White dwarfs
4.2.2 Hot subdwarfs
4.3 Eclipsing binaries
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28. PHY6795O – Naines brunes et Exoplanètes
4.3 Eclipsing binaries
HR Vir
Short period: Porb=2.8 hrs
sdB + M star, i=81°
Studied since 1980
Secular variation of the period due to magnetic breaking.
Now confirmed with two planets
Mp sin i=19.2 MJ; P=15.8 yrs, a=5.3 AU, e=0.46
Mp sin i=8.5 MJ; P=9.1 yrs, a=3.6 AU, e=0.31
Periods suggest 5:3 or 2:1 resonnance
High e in line with planet-planet interactionn
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29. PHY6795O – Naines brunes et Exoplanètes
4.4 Summary
Dynamical method
Like astrometry, sensitive to long period planets.
Amplitude of the time delay (circular orbit)
Three types of objects used for timing
Pulsars
Pulsating stars (white dwarfs, hot subdwarfs)
Eclipsing binaries
Current sensus
A dozen detection so far.
Similar technque used with transit (TTV; TDV)
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3. Astrometry