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

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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) PHY6795O – Naines brunes et Exoplanètes 4. Timing

4.0 Introduction (3) Discovery status (end of 2010) PHY6795O – Naines brunes et Exoplanètes 4. Timing

4.0 Introduction (3) Discovery status (past 2010; not complete) PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

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) PHY6795O – Naines brunes et Exoplanètes 4. Timing

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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

PHY6795O – Naines brunes et Exoplanètes 4.1 Pulsars (5) PSR B1257+12 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 66.54 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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

4.1 Pulsars (6) PSR B1257+12 – Planet-planet interaction PHY6795O – Naines brunes et Exoplanètes 4. Timing

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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

PHY6795O – Naines brunes et Exoplanètes 4.1 Pulsars (8) PSR B1620-26 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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

4.1 Pulsars (10) Pulsar planetary formation mechanisms PHY6795O – Naines brunes et Exoplanètes 4. Timing

4.1 Pulsars (10) Pulsar planetary formation through gravitational instability Beer et al. (2004) PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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. PHY6795O – Naines brunes et Exoplanètes 4. Timing

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) PHY6795O – Naines brunes et Exoplanètes 4. Timing

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: 100-1000s. Include some of the most stable know, both in amplitude and phase. Ideal targets for the timing method. e.g., G117-B15A (4.3) PHY6795O – Naines brunes et Exoplanètes 4. Timing

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) PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 www.exoplanet.eu PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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 PHY6795O – Naines brunes et Exoplanètes 4. Timing

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) PHY6795O – Naines brunes et Exoplanètes 3. Astrometry