Download The Photosphere

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 radiaCon comes from this region. •  The photosphere marks the upper end of the convecCon zone, the convecCve effects of which are manifested in granulaCon paFerns on the photosphere. using Hα filter •  To understand the reason for why we receive the visible radiaCon just from photosphere we need to understand the concepts of opacity and limb-­‐darkening. Op9cal Depth and Opacity •  The opCcal depth, τυ or τλ , is a measure of the opaqueness of a medium at a given frequency. It possesses no physical units. •  The opCcal 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 absorpCon 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 absorpCon. •  When radiaCon travels radially outward through a star, the intensity of the radiaCon changes over any liFle distance, dr, due to the opacity of the material through which it travels dI = − I kλρ dr = − I dτλ where I is intensity at posiCon r. The negaCve sign indicates a loss of intensity. •  IntegraCng over the opCcal 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 liFle radiaCon from depths deeper than τλ = 1. €
Center-­‐to-­‐Limb Varia9on •  At an angle θ, we actually see down to an opCcal depth (measured along the normal ray) of only: θ An idealized case of limb darkening. The outer boundary is the radius at which photons emiFed from the star are no longer absorbed. L is a distance for which the opCcal depth is unity. High-­‐temperature (THI) photons emiFed at A will just barely escape from the star, as will the low temperature (TLO) photons emiFed at B. •  The center-­‐to-­‐limb varia;on or limb-­‐darkening, which can be seen in images of the Sun’s disk, is usually defined by the raCo where Iλ(θ) is the intensity of the solar radiaCon arising from a point on the solar disk which makes an angle θ measured between a line from the center of the Sun to the point and a line from the Sun’s center to the observer. •  The limb-­‐darkening is oVen expressed analyCcally in the linear form, where u is known as the linear limb-­‐darkening coefficient. Therefore, for a fully darkened limb, u = 1; for no limb-­‐darkening, u = 0. •  Limb-­‐darkening can be seen even in the darkened limb of white light images of the Sun. •  It varies slowly with wavelength in the conCnuum, but generally differs from one spectral line to another, because of the different opaciCes per absorbing element and the different condiCons at the atmospheric heights where the atoms contribuCng to the line are located. Iυ Models of limb-­‐darkening: computed stellar intensity for values of cos θ = 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.25, 0.2, 0.15, 0.1, 0.125, 0.1, 0.075, 0.05, 0.025, and 0.01, for images top to boFom, respecCvely (from Kurucz 1993). Frequency •  Assuming a value of T0 , the temperature at the center of the disk (not at the center of the Sun!), one can then determine a series of values of T vs. τ and thus provide informaCon about the thermal structure of the solar atmosphere. Disk-­‐center temperature of the Sun T0 ≈ 6050 K, corresponding intensity is I0¤ ≈ 2.41 x 1010 erg cm−2 s−1 sr−1 •  In the solar photosphere, the temperature increases inward. The temperature minimum is reached in the photosphere at the base of the chromosphere, above which it climbs to very high values. •  In the ultraviolet, the center-­‐to-­‐limb variaCon shows more complicated behavior. This reflects the effect of the temperature reversal in the chromosphere and the possibility of contribuCons of atoms and ions from more than one level of the solar atmosphere. Granula9on and the Convec9on Zone •  The photosphere lies on an extensive convecCon zone, in which rising parcels of gas expand and cool and descending parcels are compressed and become hoFer. •  Typical cell size about 1000 km, known as granules (1.5 arcsecs in angular measure, lasCng ~15 minutes, largest granules last longest). The upward speeds of the hot gas in these granules is ∼500 m/s. •  This gas radiates as it nears the surface, cools, and sinks back down at the edges of the convecCve cells. These narrow cell boundaries appear darker by contrast. •  Larger regions called supergranules, sizes up to 30000 km (lasCng ~30 hours). Although the upper velociCes of these moCons are smaller, they connect the magneCc fields in the lower chromosphere into networks. Image is taken with Swedish Solar Telescope, showing a sunspot group and surrounding granulaCon. Spot umbra Spot penumbral filaments Solar granulaCon. Bright regions are about 400 K hoFer than the darker regions. Supergranules Upward regions Downward regions The chromospheric network •  ConvecCon arises if the change in pressure with temperature through the stellar atmosphere is larger than the change would occur in a parcel of gas that rises adiabaCcally, i.e, without heat loss. Such an effect can occur when there is strongly absorbing material. •  At the core of the Sun, the temperature is expected to be ∼15x106 K, and the energy created through nuclear reacCons is radiated away from the inner 0.25 R¤. •  At a distance of ∼0.71 R¤ from the center, the temperature has dropped to ∼2x106 K. The increased opacity deep in the envelope of the Sun triggers the start of the solar convecCon zone. Other Photospheric Features Source of photospheric opacity In the Sun’s photosphere, where T=6400K, there are neutral atoms (of H, He, etc.) and some ions (once-­‐ionized Na, Mg, Fe) and free electrons e-­‐. •  The free electrons aFach themselves to neutral H atoms to form a nega9ve hydrogen ion, H-­‐ : H + e-­‐ → H-­‐ •  Then an H-­‐ ion absorbs photons with hν energies at λ < 1600nm, H-­‐ + hν → H + e-­‐ •  In the photosphere, there are only 2 out of 108 hydrogen atoms is in the form of H-­‐, but this is sCll enough to be the main cause of solar opacity (that is, the absorpCon of photons). 14 •  Above the outer edge of the convecCon zone, one of the principal sources of opacity in the solar photosphere is the absorpCon of radiaCon by the H− ion, a hydrogen atom to which a second electron has been loosely aFached. •  MagneCc fields are observed on the face of the Sun; they probably arise from the convecCve moCons of charged parCcles and become amplified close to the surface. •  The overall field of the Sun is relaCvely weak: ∼10−4 Tesla (1 Gauss). This can be compared to the value at the Earth’s surface, ∼4x10−5 T (0.4 Gauss). •  From Cme to Cme, localized regions of strong magneCc fields appear at low to mid-­‐laCtudes. •  These fields inhibit convecCon and result in cooler and thus darker areas than the surrounding photosphere. •  We know these darker areas as sunspots. The numbers of, and total area occupied by, sunspots vary with a period of about 11 years. The detailed structure of the Sun in the vicinity of the spots. An acCve sunspot group (AR 8971) as recorded in the Hα spectral line on April 27, 2000, with the McMath–Pierce Solar Telescope at the KiF Peak NaConal Observatory, Arizona. The area covered is 100x100 arc-­‐secs. The strong influence of magneCc fields shapes the structure. A flare can be seen in progress on the right.