Download The Sun and the Solar System

The Sun and the Solar System •  The inves)ga)on of the nature of the solar system points to several striking facts: •  Visually the Sun is the solar system’s dominant object; it is a star, a self luminous body, powered by nuclear reac)ons in its core. •  The solar rota)on and the revolu)on of all the planets are in the same sense: counter clock wise (CCW) as viewed from the north eclip)c pole (NEP). •  The orbits are very nearly coplanar (the biggest departures being for the innermost and the outermost (usually) planets—Mercury and Pluto); and, again except for Mercury and dwarf and minor planets, very nearly circular; the spacing of the planets is not random, but is described by the Ti#us–Bode law: r = 2n x 0.3 + 0.4 Ti#us–Bode law: where n = −∞, 0, 1, 2, 3, . . . 6 (7–9, Neptune–Eris, are not well represented). •  Although the mass is strongly concentrated in the Sun, the angular momentum is concentrated in the planets, mainly Jupiter. •  The coplanar revolu)ons of the planets and the solar rota)on already make a disk forma)on of the solar system more likely. •  The low orbital eccentrici)es of the planets strengthen the case. The circularity of Neptune’s orbit, the outermost and thus least strongly bound of all the major planets (Pluto, Eris, and other “dwarf planets” excepted from this category), is especially compelling. •  There is a debris field (asteroid belt) and evidence for clouds of (cometary) debris beyond the orbit of Neptune. •  There is evidence for differen)a)on in chemical composi)on across the solar system. The Sun as a Star in the Milky Way Galaxy •  The Sun, which makes up about 99.9% of the mass of our planetary system, is a typical stable Main Sequence dwarf star of spectral class G2. It pursues an orbit about the center of the Galaxy with a radius of roughly 8 kpc and a period of about 200 million years. •  The Sun rotates approximately every 26 days around an axis inclined 7° 10’.5 to the axis of the eclip)c (which is defined by the plane of the Earth’s orbit). •  The mass of the Sun M¤ = 1.99 x 1033 g represents 99.9% of the total mass of the solar system. From the mass and the radius of the Sun, we find its mean density, < ρ > = M/[4/3πR¤3] = 1.409 g cm-­‐3 and the gravita)onal accelera)on at the solar radius R¤=6.96x1010cm, g¤ = GM¤/R¤2 = 2.7398 x 104 cm s-­‐2 •  Another important physical property is the solar angular momentum La¤, La¤= I.ω = 1.63 x 1048 g cm2/s where I is the moment of iner)a, which for a uniform sphere of mass M and radius R is I = 2/5 . MR2 where ω is the mean angular velocity ω = 2π/Prot Prot is the rota)on period. •  The overall angular momentum of the en)re solar system is, however, Ltotal = 3.148 x 1050 g cm2/s, so that La¤/Ltotal ≈ 0.005 •  Thus the angular momentum of the Sun makes up a negligible part of the total angular momentum! •  The angular momentum budget for the Solar System is dominated by the orbital angular momentum of the planets. •  The orbital angular momentum of Jupiter, LJupiter = 2 x 1050 g cm2/s •  Jupiter’s orbital mo)on carries about half the total angular momentum of the Solar System and the Jovian planets together make up 99.27% of the total. Observable Proper=es of the Quiet Sun •  Direct imaging observa)ons across the electromagne)c spectrum, in addi)on to eclipse observa)ons, reveal that the Sun’s outer regions consist of three parts: –  The photosphere (literally “sphere of light”) –  The chromosphere (“sphere of color”) –  The corona or halo •  The solar constant is the flux of total radia)on received outside the Earth’s atmosphere per unit area at the mean distance from the Sun. It is equal to C = 1.36 x 106 erg cm−2 s−1 where we have used a script C to represent the solar constant. •  The luminosity can then be determined by mul)plying the solar constant by the total surface area of a sphere of radius 1 AU: L¤ = 4πr2C = 3.826 x 1033 erg s-­‐1 •  Another way to determine the luminosity is to mul)ply the surface area of the Sun by its surface brightness. From these data, the mean solar surface brightness (flux=F) and the mean solar intensity (I) can be determined: F¤ = S = 6.27 x 1010 erg cm−2 s−1 I = F/π and, I¤ = 2.0 x 1010 erg cm−2 s−1 sr−1 •  And Sun’s the effec)ve temperature can be computed, Teff = 5780K •  The observed visual (V) magnitude of the Sun is mV = −26.75 and its color index (B-­‐V) = 0.65. •  The absolute magnitude is the magnitude of a star as it would appear at a distance of 10 pc. Therefore, M = m − 5 log(d/10) where d is expressed in parsecs. MV = 4.82. •  The bolometric correc)on (BC) is the difference between the visual and bolometric magnitudes. And it is always nega)ve, if non-­‐zero, : Mbol = MV + BC •  The bolometric correc)on for the Sun is −0.08 so its bolometric absolute magnitude is 4.74. The Photosphere •  The visible surface of the Sun is known as the photosphere (see figure). •  We see it through the overlying chromosphere and corona. •  The total thickness of the photosphere Image taken during the eclipse is about five hundred kilometers, yet most of the visible radia)on comes from this region. •  The photosphere marks the upper end of the convec)on zone, the convec)ve effects of which are manifested in granula)on pa{erns on the photosphere. using Hα filter •  To understand the reason for why we receive the visible radia)on just from photosphere we need to understand the concepts of opacity and limb-­‐darkening. Op=cal Depth and Opacity •  The op)cal depth, τυ or τλ , is a measure of the opaqueness of a medium at a given frequency. It possesses no physical units. •  The op)cal depth is zero (0) at the surface of the star, and increases with geometrical depth. •  We can also write the expression in wavelength domain τλ z
τ λ (z) = − ∫ kλ ρdz
R∗
where kλ is absorp)on coefficient and generally referred to as opacity € and/or the physical length is great, τ is also large •  When kλρ is large λ
and so is the absorp)on. •  When radia)on travels radially outward through a star, the intensity of the radia)on changes over any li{le distance, dr, due to the opacity of the material through which it travels dI = − I kλρ dr = − I dτλ where I is intensity at posi)on r. The nega)ve sign indicates a loss of intensity. •  Integra)ng over the op)cal depth, we can express the intensity, I, emerging from a column somewhere on the disk of a star, in terms of that at the base of the column, by −τ
I = I0e( λ )
•  We see li{le radia)on from depths deeper than τλ = 1. €