T Blackbody, Spectra d (age) - Astronomy Research Centre ...venn/A250/A250w5-2016.pdf · Blackbody,...

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Transcript of T Blackbody, Spectra d (age) - Astronomy Research Centre ...venn/A250/A250w5-2016.pdf · Blackbody,...

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T d L R (age) M

Blackbody, Spectra Radio Waves Venus Flux at Earth * 4π d2

Geometry, L = σT4 4π R2 (radioactive dating of rocks) orbits of planets (see Ch. 3.1.3)

5790 K 1.5 x 1011 m 3.8 x 1026 W 7 x 108 m 4.6 x 109 yr …

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Mass of the Sun : use planetary orbits

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T d L R (age) M 𝛒

Blackbody, Spectra Radio Waves Venus Flux at Earth * 4π d2

Geometry, L = σT4 4π R2 (radioactive dating of rocks) orbits of planets (see Ch. 3.1.3) avg density

5790 K 1.5 x 1011 m 3.8 x 1026 W 7 x 108 m 4.6 x 109 yr 2.0 x 1030 kg 1400 kg m-3

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MIZAR

Reference frame of one star

Stellar masses are determined from binary stars

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Spectroscopic Binary Stars

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Radial Velocity Curves for a spectroscopic binary system

Velocities measured from spectral Doppler shifts (recall Δλ/λ = v/c) - a velocity can be determined for each star in a spectroscopic binary- a variety of spectral lines are used since the whole spectrum shifts- can you tell which star is more massive from this plot?

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Eclipsing binary stars

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Eclipsing binary stars

Timing is valuable - you can tell when the eclipse starts and ends- you can tell how long it takes the secondary to cover the primary- you can tell how long the secondary is eclipsed by the primary- can you tell which star is hotter from this plot?

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For all non-eclipsing binaries, inclination angle is important!

defined as angle between sight line and thenormal to the binary orbital plane

i = 0 deg i = 60 deg

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Main Sequence Stars

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HRD for the solar Luminosity Functionneighbourhood

Because L (Mv) is related to Mass(for main sequence dwarf stars)

then this can also be shown as an initial mass function (IMF)

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M3

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Arches Cluster

supermassive star cluster at the Galactic Centre that contains several of the highest mass stars in the Milky Way Galaxy

ESO VLT NACO (IR image)

R136

supermassive star cluster at the Large Magellanic Cloud (galaxy), that contains the highest mass stars.

HST/WFC3 (U,B, V, I, H-alpha)

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The Nobel Prize in Physics 2015 recognizes

Takaaki Kajita in Japan and

Arthur B. McDonald in Canada

Takaaki Kajita presented the discovery that neutrinos from the atmosphere switch between two identities

on their way to the Super-Kamiokande detector in Japan.

The research group in Canada led by Arthur B. McDonald could demonstrate that the neutrinos from the Sun

were not disappearing on their way to Earth. Instead they were captured with a different identity when arriving to the Sudbury Neutrino Observatory.

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P P

Solar Model depends on Hydrostatic Equillibrium

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Hydrostatic Equillibrium requires a Pressure gradient

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“Solar Model”

Core • nucleosynthesis; 4H burn into He • releases nuclear binding energy

Radiative Zone • photons diffuse outward • multiple scatterings deposit energy into gas,

which lowers radiative T

Convective Zone • energy transported by mass motions of • gas (bubbles rising & falling) • steep T gradient

Surface Layers • photosphere, chromosphere, corona • region where the spectral lines form.

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Colour : 12 micron IRAS satellite map Contours: 1420 Hz DRAO continuum emission

An important implication of HSE is that gravitational potential energy is linked to internal (kinetic) energy :

True for Sun or a forming star.To show this take the equation for HSE and multiply by V :

[ dP/dr ] * V = - [ G M(r) ρ(r) / r2 ] * V

Can show that the RHS becomes

≡ 1/3 * Egr

Egr is the gravitational potential energy of a star, i.e., the energy required to assemble it by bringing matter (each shell) from infinity. ( = Ω )

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On the LHS: ∫ V dP = (integrate by parts)

= - <P> V = - N k T

Recall that internal (kinetic U) energy is Ekin = U = 3/2 * N k T

Thus, LHS = - 2/3 Ekin

Equating LHS and RHS -2/3 Ekin = 1/3 Egr or U = - Ω/2

This is a form of the virial theorem : an equation that relates the kinetic energy (U=Ekin) of a stable system consisting of N particles averaged over time, bound by potential forces, with that of the total potential energy.

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1. Stars have negative heat capacity,

U(total) = Ω + U(kin) U(total) = -2U(kin) + U(kin) U(total) = -U(kin) Thus when system loses E, such as radiation, kinetic energy increases.

2. As a star collapses (forming or evolving) then half Ω is converted into U.

What happens to the other half?

3. If the other half is converted into light, then virial theorem implies

dU/dt = dE(rad)/dt = L

Implications of U = - Ω/2

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“Solar Model”

Core • nucleosynthesis; 4H burn into He • releases nuclear binding energy

Radiative Zone • photons diffuse outward • multiple scatterings deposit energy into gas,

which lowers radiative T

Convective Zone • energy transported by mass motions of • gas (bubbles rising & falling) • steep T gradient

Surface Layers • photosphere, chromosphere, corona • region where the spectral lines form.

Testable Prediction: neutrino flux tests the nuclear reaction rate in the Core.

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x2

- all three PP chains operate simultaneously but the PP I chain occurs 69% of the time in the Sun

Proton-Proton Chain

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Neutrino Experiments

Wikipedia : “non-exhaustive list” includes 35 experiments ...

Important examples:

1. Homestake chlorine expt: 37Cl + νe → 37Ar* + e- CC 814 eV 1967-1998 - underground, isolate the Ar*, radioactivity measured ( τ 1/2 = 35 d) - 2.5 +/- 0.2 SNU (1 SNU = 1 neutrino interaction per s per 1036 targets) - 8 predicted from the solar model

Experiment flawed? No

2. (Super-)Kamiokande: Cherenkov radiation, directional detections. νe + e- → νe + e- ES 7.5 MeV 1986-1995

νe + p → e+ + n CC 1996 νe + n → e- + p CC 1996

Solar Model flawed? No - else the Sun is not in HSE (L constant).

3. Sudbury Neutrino Obs: 1999-2006 first to detect all three neutrino families νe + 2D → 2p + e− CC

νx + 2D → νx + n + p NC (works on all 3 types: no Cherenkov emission)νe + e− → νe + e− ES (works on all 3 types, but electron neutrino dominates)

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Sudbury Neutrino ObservatoryMikheyev-Smirnov-Wolfstein effect = neutrino oscillations

- there are 3 families of neutrinos (electron, muon, tau) - presence of electrons change the energy states of neutrinos thru weak interactions. - cross sections depend on neutrino mass2

mass ( νe ) << mass ( νµ ) << mass ( ντ )

< 2.2 eV/c2 < 170 keV/c2 < 15.5 MeV/c2

SNOLAB showed the low fluxes due to MSW effect: - solar model predicts only electron neutrinos - yet SNOLAB detected all three families coming from the Sun - fluxes as predicted by MSW (neutrino oscillations)

SNOLAB uses heavy water instead of cleaning fluid, to detect all three neutrino families.

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