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ASTR 200 : Lecture 13 Basic Properties of Stars 1 Once you get past the Oort cloud, we reach empty interstellar space Scales 1 au : Earth-Sun semimajor axis 5 au : Jupiter's semimajor axis, start of outer Solar System 30 au : Neptune's semimajor axis, end of planetary system 30-1000 au : The Kuiper Belt 1000 au – 50,000 au : The Oort cloud How far away are the stars? How can one measure it??? 2 3 4 5 How can one measure the distance to, or size of, a point of light??? • What can we directly observe about a star? – It's position on the sky • Maybe parallax, if close enough • Proper motion, if star is close and moving fast – The radiation we receive • Incident flux • Spectrum – Allows measurement of radial motion – Allows surface T to be estimated – Provides compositional information – Even provides rotational information 6 Direct distances to stars (parallax) Recall that a nearby star's distance is related to the parallactic angle due to the annual motion of the Earth: ('') = 1 / d(pc) 7 8 Stars within about 10 pc ~ 30 light years from the Sun Hipparcos satellite Measured good parallaxes out to ~100 pc 9 Gaia space mission Will measure parallaxes 'this half of the galaxy' 10 Stellar motions The star's true motion (or star's velocity VS) can be decomposed Into two perpendicular components: The radial velocity VR (>0 if away) the tangential velocity VT, when observed at distance d generates a `proper motion' (angular rate) μ = VT/d 11 (typically given in ''/year) A close star will appear to slowly shift 12 Barnard's Star Close by, AND fast moving Proper motion is roughly North by 20 ''/year 13 Barnard's Star Close by, AND fast moving Proper motion is roughly North by 20 ''/year Notice the annual parallax superposed here! (leftright motion) 14 15 Stars within about 10 pc = 30 light years from the Sun Radial motion: from the Doppler effect 16 The Doppler Effect The (nonrelativistic) doppler effect relates the observed wavelength λo of a wave (in this case a spectral line) to that emitted λe in the lab, and the radial speed vr of the emitter relative to the observer λ −λ v o e r Δλ = = λe λe c SIGNS note: vr> 0 is for motion APART, giving λo > λe UNITS note: Need v and c in the same units; if one uses consistent units for wavelengths, all will be OK. 17 So, can measure speeds of CARS! 18 The Doppler Effect 1. Light emitted from an object moving towards you will have its wavelength shortened. BLUESHIFT 2. Light emitted from an object moving away from you will have its wavelength lengthened. REDSHIFT 3. Light emitted from an object moving perpendicular to your lineofsight will not change its wavelength (unless v~c, in which case use relativistic). 19 The Doppler shift for light 20 So, can measure speeds of STARS! 21 Measuring Radial Velocity We can measure the Doppler shift of emission or absorption lines in the spectrum of an astronomical object. Can calculate the velocity of the object in the direction either towards or away from Earth. (radial velocity) 22 Measuring Rotational Velocity 23 Called 'rotational broadening' of spectral lines The Doppler shift for light 24 The relativistic Doppler effect Once the emitter/observer distances are changing by speeds that become a nonnegligible fraction of the speed of light, the previous formulation is only a firstorder approximation Derivation requires special relativity, due to time dilation. We will just use the result, for a light emitter moving a speed v away from an observer, that: 1+ v / c √ λ o =λ e √ 1−v / c Notice that as v approaches c, the observed wavelength o goes to infinity. The `redshift' z is defined as : 25 λ o −λ e z≡ λe Stellar Temperatures, from spectra Can match full stellar spectrum to a 'best fit' blackbody. eg: Sun's spectrum (red) Inverse wavelength (cm1) Sometimes, this fitting is complicated by the many spectral lines present. so a 'best' match is a bit of an art... stars are not perfect blackbodies in any case. 26 Example of estimating stellar radii The nearby star 'Sirius A' has a surface temperature T~10,000 K and a flux of arriving radiation at Earth (integrated over all wavelengths) of : F = 1.2 x 107 W/m2 From measurement of parallax, the distance is r = 2.64 pc = 8.1x1016 m The energy output of the star, as it washes over the Earth, is spread out over a sphere of surface area 4r2, so the total intrinsic luminosity is L = 4 r2 F = 1.0 x 1028 W = 26 solar luminosities This then allows us to get the stellar radius R, because under the assumption that the star radiates like a black body, L = 4 R2 T 4 so solving for R and plugging in gives: R = 1.7 solar radii So Sirius A is a star about twice as hot and twice as big as the Sun. Note that because L varies as the 4th power of T, this makes the 26x luminosity 27 Stars near the Sun tend to be equal size or smaller 28 But some are MUCH larger than the Sun 29