# Astronomy 217

## Prof. Andrew W. Steiner

Oct. 11, 2021

TA James Ternullo

## Today

• Solar Observations

## The Visible Sun

• We study the Sun for 2 reasons.
• The Sun influences the Earth, providing it with sunlight, striking it with the solar wind.
• The Sun is the nearest star, our best chance to study a star up close. It was the only star whose image can be resolved and from which we collect neutrinos.

## Luminosity

• Luminosity is the total energy radiated by the Sun.
• The amount of Sun's energy reaching Earth is called the Solar constant.
• The mean solar constant is about $1400~\mathrm{W}/\mathrm{m}^2$.
• The Sun’s Luminosity, $L_{\odot}$, can be calculated from the Solar constant and the Earth’s orbital separation.
• $L_{\odot} =4 \times 10^{26}~\mathrm{W}$, equivalent to 100 billion megatons of TNT per second

## Solar Spectrum

• Sunlight also tells us the composition of the Sun.
• Spectral analysis, beginning with Fraunhofer in 1814, exhibits lines from 67 different elements.
• Among these is helium, which was discovered by Norman Lockyear in 1868 in the spectrum of the chromosphere.
• Helium was isolated terrestrially in 1895.
• More than 90% of the atoms are hydrogen, 9% He and 0.13% “metals”

## Photosphere

• The visible surface of the Sun, or any radiating body, is the photosphere. The photosphere occurs at the point in the star where the optical depth, $\tau = \sigma(x) n(x) x$ approaches 1.
• This filtered image of the Sun shows a sharp edge to the Sun, telling us the Sun’s photosphere is very thin.
• The radius of the photosphere is 696,000 km (commonly equated to the radius of the Sun, $R_{\odot}$), but the photosphere is ~ 400-500 km thick.
• A blackbody of T = 5700K best fits the Sun’s photosphere.

## H- Ions

• The thinness of the solar photosphere, and its relative independence of wavelength, are the result of H− ions that occur for 2500 K < T < 10000 K.
• In this range of temperature, collisional ionization occurs for many metals with low ionization potentials, but not for H, with a 13.6 eV ionization potential.
• Hydrogen atoms combine with free electrons to make H− ions, which have an ionization potential of 0.75 eV. Thus H− can absorb any photon whose energy is greater than 0.75 eV, corresponding to λ = 1.7 μm.
• For lower densities, H + e− collisions do not occur frequently enough to compete with photo-ionization, making a sharp cutoff in radius to the H− opacity.

## Limb Darkening

• The reduced intensity around the edge, or limb, of the solar disk is called limb darkening.
• As one moves away from the center of the solar disk, the radius reached for a given column depth is reduced by the oblique angle.
• Since the temperature increases toward the center of the Sun, $T_B<T_A$, are seen on the limb.
• With $I \propto T^4$, the limb can be as much as 1/10 as bright.

## Solar Granulation

• A closer look at the photosphere reveals a pattern of granulations, typically 1000 km across, that change on a 10 minute timescale.
• These granulations are the visible top layer of the convection zone, with areas of hotter upwelling material ($1~\mathrm{km}~\mathrm{s}^{-1}$) surrounded by areas of cooler sinking material.

## Solar Structure

• The peaking of the convective zone through the photosphere hints at the complicated interior structure of the Sun, which we will cover later.
• Today, we’re focused on the visible parts of the sun, the solar atmosphere.
• Above the photosphere lie 3 progressively less dense regions, the Chromosphere, the Transition Zone and the Corona.

## Solar Magnetism

• Key to understanding the behavior of the Sun’s atmosphere is the motion of fluid in a magnetic field.
• A moving charge in a magnetic field experiences the Lorentz Force $$\vec{F}_L = q \vec{v} \times \vec{B} = q \left( \vec{v}_{\perp} + \vec{v}_{\parallel} \right) \times \vec{B}$$
• Motion along the magnetic field is unchanged, but motion perpendicular causes an acceleration $$a = \frac{q}{m} v_{\perp} B$$
• This acceleration pushes the particle in helical orbit of radius $$r_c = \frac{m v_{\perp}}{q B}$$ (the Larmor radius)

## Magnetic Energy

• A magnetic field with strength $B$ has an energy density $$E_B = \frac{B^2}{2 \mu_0}$$ and an equivalent pressure $$P_B = \frac{B^2}{2 \mu_0}$$
• In terms of a 1 Tesla field: $$P_B = 4 \times 10^5~\mathrm{N}~\mathrm{m}^{-2} \left( \frac{B}{1~\mathrm{T}} \right)$$
• For comparison, the thermal gas pressure is $$P_{\mathrm{gas}} = n k T = 5 \times 10^{3}~\mathrm{N}~\mathrm{m}^{-2} \left( \frac{\rho}{10^{-4}~\mathrm{kg}~\mathrm{m}^{-3}} \right) \left( \frac{T}{6000~\mathrm{K}} \right)$$ The importance of magnetic phenomenon in the gas can be deduced by comparing $P_B$ to $P_{\mathrm{gas}}$

## Sunspots

• One very visible consequence of solar magnetic fields are sunspots, which move across the face of the Sun.

## Sunspots in Motion

• The Solar and Heliospheric Observatory (SOHO) orbits at Earth’s L1 point, outside the Earth’s magnetosphere measuring the Sun’s magnetic field, corona, vibrations, and ultraviolet emissions.

## Magnetic Kinks

• Sunspots, which typically last from days to months, result from loops of the Sun’s magnetic field breaking through the photosphere.

## Magnetic Cooling

• The cooler temperature in a sunspot results from the magnetic pressure.
• If we set the gas pressure outside of the sunspot equal to the sum on magnetic and gas pressure inside, $$n k T_s + B^2/\mu_0 = n K T_p$$ this gives a magnetic field strength of $$B = \left[ 2 \mu_0 n k \left( T_p - T_s \right) \right]^{1/2}$$
• For the photosphere, $\rho=3.5 \times 10^{-4} ~\mathrm{kg}~\mathrm{m}^{-3}$, thus $$n = \rho/(\mu m_p) = 2.1 \times 10^{23}~\mathrm{m}^{-3}$$ while $T_p - T_s \approx 1800~\mathrm{K}$
• This tells us the magnetic field in a sunspot is ≈ 0.1 T, 10-100 times larger than the average solar surface field.

## Differential Rotation

• As a fluid body, the Sun is not constrained to rotate rigidly. It rotates differentially, with a period near the poles of 35 days, but 25.4 days at the equator.
• The arrangement of sunspots originates from magnetic field lines distorted by this differential rotation.

## Sunspot Cycles

• The frequency of sunspots follows an 11 year cycle.
• However, the maximum amplitude between cycles can vary significantly. During the Maunder minimum in the late 1600s, few, if any, sunspots occurred.

## Sunspot Latitude

• The location of sunspots also follows the 11 year cycle, with sunspots first appearing at high latitudes early in the cycle and gradually lower as the cycle progresses.
• The cycle actually has a 22-year period, as the magnetic polarities reverse between northern and southern hemispheres every 11 years.

## Chromosphere

• Above the photosphere lies the chromosphere, with a density $10^4$ lower that the photosphere.
• The chromosphere is difficult to see directly against the brightness of the photosphere.
• However sometimes, Moon covers photosphere and not chromosphere during eclipse.
• One can also observe the chromosphere using filters to select narrow bands with strong photospheric absorption, leaving the chromospheric emission lines visible, like $H_β$ or He, which was discovered in the chromosphere.

## Chromospheric Features

• Plages: regions of strong magnetic field near sunspots.
• Prominences: cool clouds of gas following a magnetic field feature.
• Filaments: long dark features, prominences seen from above.

## Spicules

• Small scale storms in the chromosphere emit spicules, short-lived, narrow jets of $10~\mathrm{km}~\mathrm{s}^{-1}$ gas, typically lasting a few minutes.
• They appear as dark spikes sprouting up from the solar chromosphere, visible against the face of the Sun because they are cooler than the underlying photosphere.

## Corona

• The upper most layer of the Sun’s atmosphere is the solar corona.
• Solar corona can be seen during eclipse if both photosphere and chromosphere are blocked or using a coronagraph.
• The inner K corona (R < $2.5~R_{\odot}$) exhibits a continuum spectrum with emission lines, but no detectable absorption lines.
• The outer F corona exhibits a continuum with absorption lines

## Coronal Heating

• Early observations of the corona revealed a wealth of unidentified lines, and even the supposition that there were new elements in the corona.
• It was later determined that these lines came from highly ionized species, indicating that the corona is much hotter than layers below it.
• Suggestions for the heat source include photospheric sound waves and magnetically induced currents.