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The Host Stars: To know the Planet you have to know the Star Why should we care about the host stars? 1. Stellar properties give hints to planet formation • • • Abundance: The role of metals in formation Age of star: Age of planet and evolution Activity level of star: star-planet interaction, effects on habitability Why should we care about the host stars? 2. Stellar properties are important for accurate planet parameters • Doppler measurements for mass Vobs = 28.4 mp sin i P1/3 Ms2/3 • Transit light curve gives you k = Rp / Rs The inner structure of Kepler-10b and CoRoT-7b CoRoT-7b Kepler-10b r (gm/cm3) 10 7 Earth Mercury 5 4 3 Venus Mars Moon 2 1 0.2 2 0.4 0.6 0.8 1 1.2 1.4 Radius (REarth) 1.6 1.8 The inner structure of Kepler-78b The limiting factor determining our knowledge of the internal structure of these planets is the stellar parameters Why should we care about the host stars? 2. Stellar properties are important for accurate planet parameters • Limb darkening : Affects the “stellar radius” in the transit modeling • Temperature of the star : Equilibrium temperature of the planet • Distance to the star: Location of planets in our galaxy and environment Example: CoRoT-19b Spectroscopic analysis Evolutionary models lightcurve analysis Up the main sequence: 1. Higher Mass 2. Higher temperature 3. Shorter life 2 Mסּ 1 M( סּs.m.) 0.1 Mסּ Sp.T Mass (solar) Radius (solar) Teff (K) Lum. (solar) Lifetime ( years) B0 17.5 7.4 30000 200 000 3.5 x 106 B5 5.7 5.9 15200 380 1.5 x 108 A0 2.9 2.4 9790 24 1.2 x 109 A5 2.0 1.7 8180 11 1.8 x 109 F0 1.6 1.6 7300 5.1 3.1 x 109 F5 1.24 1.4 6650 2.7 4.6 x 109 G0 1.05 1.05 5940 1.2 8.8 x 109 G5 0.92 0.92 5560 0.73 1.3 x 1010 K0 0.79 0.79 5150 0.38 2.1 x 1010 K5 0.67 0.67 4410 0.15 4.5 x 1010 M0 0.51 0.51 3840 0.080 6.4 x 1010 M5 0.21 0.20 3170 0.011 1.9 x 1011 Fundamental Stellar Parameters: Distance ©Perryman 2011, fig. 8.1 • Accuracy of distances of planet host stars increased substantially from ground-based (a) to Hipparcos (b). • GAIA will improve things and give accurate distances, luminosities, and temperatures of millions of stars out to thousands of parsecs HR diagram with planet host stars • HR diagram of stars within 25 pc • based on Hipparcos data Hawley & Reid (2003), Perryman (2011; fig. 8.5) Fundamental Stellar Parameters: Mass and Radius Along the main sequence there is a tight relationship between spectral type and the stellar radius and mass. One can get estimates of the stellar radius and mass from the spectral type. This requires that the main sequence be calibrated Calibrating Stellar Masses using Astrometric Measurements of Binary Stars W 1062 AB -0.1 4 5 6 Declination (arcsec) 3 MA = 0.381 ± 0.006 MO MB = 0.187 ± 0.003 MO 0.0 8 0.1 9 90°(E) 10 11 17 16 15 0.2 2 0° (N ) -0.2 1 14 -0.1 12 0.0 RA (arcsec) 0.1 Calibrating Stellar Masses and Radii using Eclipsing Binary Stars The light curve gives you the stellar radii, Doppler measurements give you the masses of the stars Torres et al. Radius vs. Mass Radius vs. Effective Temperature Mass vs. Temperature Luminosity vs. Mass Meaurements of Stellar Radii using Lunar Occultations R = 45.1 ± 0.1 Rsun Measurements of Stellar Radii using Interferometry A Basic Interferometer S s • B = B cos q q A2 x2 A1 x1 Delay Line 1 d1 Beam Combiner 1) Idealized 2-telescope interferometer Delay Line 2 d2 Interferometry Basics Adjacent fringe crests projected on the sky are separated by an angle given by: Ds = l/B, B is the baseline Every baseline samples a new “frequency” Nulling Interferometers Adjusts the optical path length so that the wavefronts from both telescope destructively interfere at the position of the star Technological challenges have prevented nulling interferometry from being a viable imaging method…for now Darwin/Terrestrial Path Finder would have used Nulling Interferometry Earth Venus Mars Ground-based European Nulling Interferometer Experiment will test nulling interferometry on the VLTI The VLT Interferometer The Keck Interferometer Interferometry Basics: The Visibility Function Michelson Visibility: Imax –Imin V= Imax +Imin Visibility is measured by changing the path length and recording minimum and maximum values Interferometry Basics: Cittert-Zernike theorem The visibility : V(k, B) = da db A(a,b) F(a,b) e −2pi(au+bv) Cittert-Zernike theorem: The interferometer response is related to the Fourier transform of the brightness distribution under certain assumtions (source incoherence, small-field approximation). In other words an interferometer is a device that measures the Fourier transform of the brightness distribution. F(a,b) is flux distribution of object on sky Aperture Synthesis Aperture Space V N B E Spatial Resolution : l/B Can resolve all angular scales up to q > l/D, i.e. the diffraction limit Fourier Space U Frequency Resolution : B/l Can sample all frequencies out to D/l One baseline measurement maps into a single location in the (u,v)-plane (i.e. it is only one frequency measurement of the Fourier transform) Aperture Synthesis Consider a 2-telescope array B2 B1 B4 B3 = Interferometry Stellar Angular Diameters: V(s) = |2J1(pas)/pas| J1 is the first order Bessel function Note: as it should be, this is also the diffraction pattern of a circular aperture. Diameters of Giant Stars The Radius of HR 8799 R = 1.44 ± 0.06 RSun L = 5.05 ± 0.29 LSun Teff = 7193 ± 87 K Baines et al. The Radius of Epsilon Eridani R = 0.74 ± 0.01 RSun Teff = 5039 ± 126 K Stellar Diameters of Giant Stars Measuring Stellar Atmospheric Parameters: Temperature, surface gravity, abundance of heavy elements Simple Way: Compare observed spectra with library of known stars with well determined parameters • Simple, but limited accuracy • One still has to determine the stellar parameters for the library spectra! Use temperature Sensitive Lines: Sodium T = 5100 K T = 7300 K The strength of Na D decreases with increasing temperature. Behavior of Hydrogen lines with temperature B3IV B9.5V A0 V G0V F0V The atomic absorption coefficient of hydrogen is temperature sensitive through the Stark effect. Because of the high excitation of the Balmer series (10.2 eV) this excitation growth continues to a maximum T = 9000 K Comparison of Interferometric Temperatures with Spectroscopic Temperatures for giant stars L = sT4(4pR2) Behavior of Spectral Lines: Abundance Dependence The line strength should also depend on the abundance of the absorber, but the change in strength (equivalent width) is not a simple proportionality as it depends on the optical depth. 3 phases: Weak lines: The line strength increases proportional to the abundance of the element Saturation: Line depth (strength) approaches a constant value Strong lines: The wings start to grow and the line strength increases, but not proporinally The graph specifying the change in equivalent width with abundance is called the Curve of Growth Surface Gravity: GM/R2 Use gravity sensitive lines like Fe II 4508 Å Stellar Gravity from the Transit Duration t = 2(R* +Rp)/v where v is the orbital velocity and i = 90 (transit across disk center) For circular orbits v = 2pa/P From Keplers Law’s: a = (P2 M*G/4p2)1/3 2R* P (4p2)1/3 t 2p P2/3 M*1/3G1/3 t R* /M*1/3 This is the „transit gravity“ and is often used to check the value from spectroscopy. Best way: Model the spectrum Set of stellar parameters: Teff, logg, [M/H],... Model atmospheres: e.g. ATLAS9, MARCS, MAFAGS Temperature profile Pressure profile ... Line formation codes: e.g. SPECTRUM, MOOG, LINFOR Synthetic spectrum The „Metal“ Abundance of Exoplanet Host Stars The „Bracket“ [Fe/H] • e.g. [Fe/H] = –1 → 1/10 the iron abundance of the sun • unit: „dex“ (contraction of decimal exponent, indicates decimal logarithmic ratio which is in fact unitless) • [Fe/H] is often used as an overall metallicity indicator, other elements then are related to Fe, e.g. [Mg/Fe]. The Star-Metallicity Connection Astronomer‘s Metals More Metals ! Even more Metals !! Metallicity correlation • host stars of planets appear on average more metal-rich than comparison stars without planets • probability to find planet is higher for metal-rich star Santos et al. (2005) The Planet-Metallicity Connection Valenti & Fischer There is believed to be a connection between metallicity and planet formation. Stars with higher metalicity tend to have a higher frequency of planets. This is often used as evidence in favor of the core accretion theory Limb Darkening Temperature Bottom of photosphere Temperature profile of photosphere 10000 8000 6000 4000 q2 q1 z=0 tn =1 surface Top of photosphere z dz The path length dz is approximately the same at all viewing angles, but at larger the optical depth of t=1 is reached higher in the atmosphere Report that the transit duration is decreasing with time, i.e. the inclination is changing: However, Kepler shows no change in the inclination! One solution: Mislis et al. had to combine data taken from different instruments with different filters, i.e. observed at different wavelengths. An improper treatement of limb darkening will make the transit duration different. Limb Darkening Laws used by Transit Light Curve Modelers m = cos q, q = 0 at disk center, 90o at limb Limb darkening for stars other than the Sun use theoretical model atmospheres Stellar activity Sun in Ca II K: chromosphere! Sun in white light: photosphere Stellar Flares Stix (1991, pp. 352, 355) Stellar (chromospheric) activity is often meaured using the Ca II H & K resonance line: Active Star Inactive Star Ca II line 5 Minutes of Stellar Atmospheres: Optical depth, t : How far you can see in the atmosphere. t large: You are looking high up in the atmosphere (photons are readily absorbed so they cannot make it out) t small: Photons can travel a long way before being absorbed, i.e. you can see deeper into the atmosphere Source contribution function: Where the photons are coming from Sample Contribution Functions Strong lines Weak line On average weaker lines are formed deeper in the atmosphere than stronger lines. For a given line the contribution to the line center comes from deeper in the atmosphere from the wings Two important rules: 1) Strong spectral lines are formed higher up in the stellar atmosphere than weak lines. 2) The core of the line is formed higher up than the wings Temperature profile of a solar like active star Chromosphere Dl (Å) Core formed here where temperature is higher Photosphere Wing formed here Strong absorption lines are formed higher up in the stellar atmosphere. The core of the lines are formed even higher up (wings are formed deeper). Ca II is formed very high up in the atmospheres of solar type stars. Measurement: S-Index/R’HK •measure flux in emission line f(H) and f(K) Active star Inactive star •absolute flux in H and K of active star: •subtract photospheric contribution Fphot based on model atmosphere or inactive standard: Strassmeier (1997), pp. 249, 250 Measurement principle Active star • absolute flux in H and K of active star: Inactive star Strassmeier (1997), pp. 249, 250 Activity-related RV The RV scatter (“jitter”) is correlated with the level of activity Saar et al. (1998, ApJ 498L, 153) Star-Planet Interaction Shkolnik et al. 2003 Determining the Age of a Star Evolutionary Tracks Girardi tracks : http://stev.oapd.inaf.it/cgi-bin/param HR 8799 M = 1.51 ± 0.24 MSun Interferometric R and T Age = 30 Million Years e Eridani M = 0.82 ± 0.05 MSun Interferometric R and T Age = 109 years Magnetic braking • convection + rotation are thought to generate magnetic field via stellar dynamo (Gray, 2005, pp. 490-492) • stars with convective envelopes form a magnetic field • stellar wind is coupled to magnetic field lines and thus to stellar rotation • therefore, stellar wind takes away angular momentum and the stellar rotation is braked Magnetic braking formation of convective envelope Gray (2005), p. 485 Indicators of Stellar Youth 1. Rapid rotation in cool star: The star has not had enough time to slow down through magnetic braking 2. High level of activity (Ca II emission): Related to (1) as stars that rotate rapidly also generate more magnetic fields 1. Strong lithium line. Lithium is destroyed at temperatures of a few million K. The star starts with lithium present, but through time convection brings it to the bottom of the convection zone where it is destroyed Broad lines are from a young a star Narrow lines are the sun Dl (Å) The Lithium Line The strength of the Lithium line can be calibrated with age, but it is generally not that good. In a solar type star the presence of Lithium most likely means it is young. But the processes that affect the strength of lithium are poorly known. For instance, strong Li is also found in some evolved giant stars! Skumanich Law Ca II emission in stars from several clusters. For older clusters the emission levels off and it is difficult to get an accurate age Asteroseismology: The best way to get the important stellar parameters Zonal mode Sectoral mode Low degree modes High degree modes Red: high degree modes have shorter wavelengths and do not propagate deeper into the sun. Decreasing density causes the wave to reflect at the surface Increasing density causes the wave to refract in the interior. Blue: low degree modes have longer wavelengths and propagate deeper into the sun. The Asymptotic Limit for p-mode Oscillations For high order modes: n >> l nn,l = Dn0 (n + l /2 + e) Dn0 = large spacing D0 is sensitive to the sound speed near the core e is sensitive to the surface layers Modes are separated by odd and even degree (l). The socalled large separation is between sequential odd/even modes. What we see is one-half the large spacing) The Solar Power Spectrum nmax ≈ 3000 mHz Dn0 ≈ 135 mHz How do we scale these to other stars? Large spacing Summary of Scaling Relationships vosc L/Lסּ = (23.4 ± 1.4) cm/sec M/Mסּ ( ( dL L l = (l/ 550 nm) (M/M)סּ1/2 Dn0 = nmax L/Lסּ 134.9 3/2 (R/R)סּ M/Mסּ = (R/Rסּ )2√T eff/5777K (4.7 ± 0.3) ppm (Teff / 5777 K)2 mHz (M/M)סּ The large frequency spacing is related to the mean density of the star 3.05 mHz Asteroseismology of the 16 Cyg A and 16 Cyg B (planet hosting) Figure 1 from Asteroseismology of the Solar Analogs 16 Cyg A and B from Kepler Observations T. S. Metcalfe et al. 2012 ApJ 748 L10 doi:10.1088/2041-8205/748/1/L10 Stellar Oscillations in b Gem Nine nights of RV measurements of b Gem. The solid line represents a 17 sine component fit. The false alarm probability of these modes is < 1% and most have FAP < 10–5. The rms scatter about the final fit is 1.9 m s–1 The Oscillation Spectrum of Pollux The p-mode oscillation spectrum of b Gem based on the 17 frequencies found via Fourier analysis. The vertical dashed lines represent a grid of evenlyspaced frequencies on an interval of 7.12 mHz Frequency Spacing M1/2 Dn0 ≈ Dn0 ≈ 135 mHz R3/2 7.12 mHz Inteferometric Radius of b Gem = 8.8 Rסּ For radial modes → M = 1.89 ± 0.09 Mסּ Evolutionary tracks give M = 1.94 Mסּ