Today in Astronomy 142: observations of stars Measurable properties of stars Parallax and the distance to the nearest stars Magnitudes, flux and luminosity Blackbodies as approximations to stellar spectra Stellar properties from stellar photometry • Colors and temperature • Bolometric correction and bolometric magnitude Open cluster M39 in Cygnus (Heidi Schweiker, WIYN/NOAO) 22 January 2013 Astronomy 142, Spring 2013 1 What do we want to know about stars? As a function of mass and age, For the visible stars, measure… find... Flux at all wavelengths, at high Structure of their interiors resolution (probes the Structure of their atmospheres atmosphere) Chemical composition Magnetic fields, rotation rate Power output and spectrum Oscillations in their power Spectrum of oscillations output (probes the interior) All the ways they can form Distance from us, and position All the ways they can die in galaxy The details of their lives in Orbital parameters (for binary between stars) The nature of their end states Their role in the dynamics and … and match the evolution in their host galaxy measurements up with theories 22 January 2013 Astronomy 142, Spring 2013 2 What do we want to know about stars? As a function of mass and age, For the visible stars, measure… find... Flux at all wavelengths, at high Structure of their interiors resolution (probes the Structure of their atmospheres atmosphere) Chemical composition Magnetic fields, rotation rate Power output and spectrum Oscillations in their power Spectrum of oscillations output (probes the interior) All the ways they can form Distance from us, and position in galaxy All the ways they can die Orbital parameters (for binary The details of their lives in stars) between The nature of their end states … and match the Their role in the dynamics and measurements up with theories evolution in their host galaxy (We can do what’s in green, this semester) 22 January 2013 Astronomy 142, Spring 2013 3 Flux and luminosity Primary observable quantity: flux (power per unit area) within some range of wavelengths. The flux at the surface of an emitting object is often called the surface brightness. Stars, like most astronomical objects, emit light isotropically (same in all directions). Since the same total power L must pass through all spheres centered on a star, and is uniformly distributed on those spheres, the flux a distance r away is fL= /4π r2 To obtain luminosity (total power output), one must add up flux measurements over all wavelengths, and measure the distance. Best distance measurement: trigonometric parallax. 22 January 2013 Astronomy 142, Spring 2013 4 July January view view Trigonometric parallax Star Relatively nearby stars appear to move back and forth with respect to much more distant stars as the Earth travels in its orbit. Since the Earth’s orbit is (nearly) r circular, this works no matter what the direction to the star. p Since the size of the Earth’s orbit is known very accurately from radar measurements, measurement of the parallax p determines the distance to AU the star, precisely and accurately. Earth 22 January 2013 Astronomy 142, Spring 2013 5 Trigonometric parallax (continued) And all stars have very small trigono- metric parallax. Suppose stars were typically a light-year away, which we’ll see to be an extreme underestimate: January pp352 tan pp=+++ 3 15 1 AU 1.5× 1013 cm = ≈ r 9.5× 1017 cm 2p − =1.6 × 105 1 , so pr≅ 1 AU July is an excellent approximation. 22 January 2013 Astronomy 142, Spring 2013 6 Trigonometric parallax (continued) Note that, in expressions such as 1 AU tanpp≅= and r , p p is understood to be measured in radians. More conveniently, parallaxes of nearby stars are reported in arcseconds or fractions thereof: π radians= 180 °= 180 × 60 × 60 arcsec =6.48 × 105 arcsec The distance to an object with a parallax of 1 arcsecond, called a parsec, is 3.0857× 1018 cm= 3.2616 ly. Good parallax measurements: about 0.01 arcsec from the ground, about 0.001 arcsec from the Hipparcos satellite. 22 January 2013 Astronomy 142, Spring 2013 7 Parallax examples What is the largest distance that can be measured by parallax with ground-based telescopes? With the Hipparcos satellite? First note that we can write the distance-parallax relation as 1 AU 1 parsec r = = . pp[radians] [ arcsec] So if the smallest parallax we can measure is 0.01 arcsec, the largest distance is 1/0.01 = 100 parsecs. Similarly, Hipparcos got out to 1/0.001 = 1000 parsecs. The ESA satellite Gaia, due to be launched in 2012, will measure parallax with an accuracy of 0.00002 arcsec, thus perhaps stretching out to 50 000 parsecs = 50 kpc. • Compare: we live 8 kpc from the center of our Galaxy. 22 January 2013 Astronomy 142, Spring 2013 8 Parallax examples (continued) If we lived on Mars, what would be the numerical value of the parsec? Mars’s orbital semimajor axis is 1.524 AU, so the parsec is a factor of about 1.524 larger: 1.524 AU r =1 "parsec" = 1 arcsec 1.524×× 1.496 1013 cm 3600 arcsec 180° = 1 arcsec 1° π =×=4.703 1018 cm 4.971 light years. But Mars’s orbit is twice as eccentric as Earth’s, so beware of those last decimal places. 22 January 2013 Astronomy 142, Spring 2013 9 The thirty nearest stars Wikimedia Commons 22 January 2013 Astronomy 142, Spring 2013 10 Secret astronomer units: magnitudes Ancient Greek system: first magnitude (and less) are the brightest stars, sixth magnitude are the faintest the eye can see. (Magnitude ⇑, brightness ⇓.) The eye is approximately logarithmic in its response: perceived brightness is proportional to the logarithm of flux. To match up with the Greek scale, 5 mag⇔ a factor of 100 in flux 15 1 mag⇔≅ a factor of (100) 2.5 in flux or, for two stars with apparent magnitudes m1 and m2, m−= m2.5log ( ff) log = log10 2 1 12 from now on 22 January 2013 Astronomy 142, Spring 2013 11 Magnitudes (continued) Most people find magnitudes confusing or even stupid at first, but they turn out to be very useful once one gets used to them. Magnitudes are dimensionless quantities: they are related to ratios of fluxes or distances. Another legacy from the Greeks: magnitudes run backwards from the intuitive sense of brightness. • Brighter objects have smaller magnitudes. Fainter objects have larger magnitudes. They’re like “rank.” Fluxes from a combination of objects measured all at once add up algebraically as usual. The magnitudes of combinations of objects do not. (See example below.) 22 January 2013 Astronomy 142, Spring 2013 12 Magnitudes (continued) The reference point of the apparent magnitude scale is a matter of arbitrary definition. As usual! Same as the meter, the second, the kilogram… The practical definition of zero apparent magnitude is Vega (α Lyrae), which has m = 0.0 at nearly all wavelengths < 20 µm. A reference that‘s hard to lose: it’s the brightest star in the northern hemisphere of the sky. So the apparent magnitude m of a star from which we measure a flux f is m=−= mmVega 2.5log ( fVega f) . Vega’s fluxes have been measured with excruciating care and are tabulated; see the Constants page on our website. 22 January 2013 Astronomy 142, Spring 2013 13 Magnitudes (continued) Two other Magnitudes are also necessary: Absolute magnitude is the apparent magnitude a star would have if were placed 10 parsecs away. Bolometric magnitude is magnitude calculated from the flux from all wavelengths, rather than from a small range of wavelengths. In Homework #1 you’ll show that the absolute and apparent bolometric magnitudes, M and m, of a star are related by M= m−=−5log( r 10 pc) 4.75 2.5log (LL ) You will now be sworn to secrecy, and henceforth may never explain magnitudes to a non-astronomer. 22 January 2013 Astronomy 142, Spring 2013 14 Magnitude-calculation examples The absolute bolometric magnitude of the Sun is 4.75. What is its apparent bolometric magnitude? That is, the Sun’s apparent magnitude is 4.75 when seen from 10 parsecs (subscript 2), but we see it from 1 AU (1): f L 4π r2 mm=+=+2.5log 2 m2.5log 1 12 2 2 fL1 4π r2 2 [1 AU] 1 AU =4.75+= 2.5log 4.75+ 5log 2 10 parsecs [10 parsecs] = −26.82 . Recall: logxx2 = 2 log . 22 January 2013 Astronomy 142, Spring 2013 15 Magnitude-calculation examples (continued) Two objects are observed to have fluxes f and f+∆ ff ( ∆ f ). What is the difference ∆m between their magnitudes? ff+∆ ∆f ∆=mm12 − m =2.5log =2.5log 1 + ff 2.5 ∆∆ff =ln 1 +≅ 1.09 to first order in ∆f . ln 10 ff Thus, if two objects differ in flux by 1%, they differ in magnitude by 0.011. It is very hard to measure fluxes from astronomical objects more accurately than 1%, so typically magnitudes are not known more accurately than ±0.01 or so. 22 January 2013 Astronomy 142, Spring 2013 16 Magnitude-calculation examples (continued) Two stars, with apparent magnitudes 3 and 4, are so close together that they appear through our telescope as a single star. What is the apparent magnitude of the combination? Call the stars A and B, and the combination C: 1 fA 2.5 0.4 mmBA−==1 2.5log ( ffAB) ⇒ =10 = 10 = 2.512 fB f ff+ f Add 1 to both sides: A+=1 AB = C =3.512 fB ff BB So mmBC−=2.5log ( ffCB) mC=−= m B2.5log( ff CB) 4−= 2.5log( 3.512) 2.64 .