Lecture 7: Radio Observations of Coronal Mass Ejections I Hale COLLAborative Graduate Education (COLLAGE) Course 2017 Prof. Bin Chen (New Jersey Institute of Technology) Lectures 7-8 outline • Radio astronomy preliminaries • Radiative transfer • Relevant emission mechanisms • Types of solar radio bursts This Lecture • Radio observations of CMEs • CME body • Thermal CME • Gyrosynchrotron CME • Type IV radio bursts • CME-driven shocks • White light/EUV imaging, UV spectroscopy, and in situ signatures • type II radio bursts 1/16/2017 2 Radiation Fundamentals‣ Essential Radio Astronomy The surface containing can be any surface,Preliminaries real or imaginary; that is, it could be the physical surface of the detector, the source, or an imaginary surface anywhere along the ray. If energy from within the solid angle flows through the projected area in time and in a narrow frequency band of width , then • Specific intensity (2.1) 1/16/2017 • Flux density2 Radiation Fundamentals‣ Essential Radio Astronomy Power is defined as the flow of energy per unit time, so the corresponding power is (2.9) • Units -2 -1 -1 • Flux density �": ergs cm s Hz If the source angular size is , and• the1 Jy expression= 10-26 ergs cm for flux-2 densitys-1 Hz-1 is much simpler: • 1 solar flux unit (sfu) = 104 Jy • Specific intensity � : ergs cm-2 s-1 Hz-1 sr-1 Thus the quantitative definition of specific intensity or spectral brightness" is • Sometimes radio images have units of Jy/beam (2.10) • Total flux: ergs cm-2 s-1 *CGS unit throughout this lecture This is usually the case for astronomical sources, and astronomers rarely use flux densities to describe sources so extended that the factor must be retained (e.g., the diffuse emission from our Galaxy). (2.2) In practice, when should spectral brightness and when should flux density be used to describe a source? If a source is unresolved, meaning that it is much smaller in angular size than the point-source response of the eye or telescope observing it, its flux density can be and the MKSmeasured units butof its arespectral brightness cannot. To. the naked eye, the unresolved red giant star Betelgeuse appears to be one of the brightest stars in the sky. Yet calling it a “bright star” is misleading because the total intensity of this relatively cool star is lower than the total Radio intensityastronomers of every almost hotter butalways more distantmeasure star frequencies,that is scarcely but visible observers to the eye. in Betelgeuse other wavebands appears “brighter” normally than measure most other wavelengths stars only rather than because it subtends a much larger solid angle and therefore its flux is higher. If a source is much larger than the point-source response, its frequencies,spectral so the brightness brightness at any per position unit wavelength on the source can be measured directly, but its flux density must be calculated by integrating the observed spectral brightnesses over the source solid angle. Consequently, flux densities are normally used to describe only relatively compact sources. (2.3) is also widely used. The MKS units of are . The relation between the intensity per unit frequency and the intensity per unit wavelength can be derived from the requirement that the power in the frequency interval to must equal the power in the corresponding wavelength interval to : (2.4) Figure 2.6: An illustration of the definition of flux density. Thus The MKS units of flux density, , are much too big for practical astronomical use, so astronomers use smaller ones: http://www.cv.nrao.edu/~sransom/web/Ch2.html 7/49 http://www.cv.nrao.edu/~sransom/web/Ch2.html 3/49 Radiative Transfer • In the absence of emission, absorption, or scattering (the “free space”), the specific intensity �" along a ray does not change. • However, if emission and absorption occurs, we use the radiative transfer equation �� " = −� � + � �� " " " -1 where �" is the absorption coefficient (units cm ) -3 -1 and �" is the emission coefficient (units ergs cm s Hz-1 sr-1). Radiative Transfer • Defining the optical depth �" = �"�� (no unit) and the source function �" = �"/�" the transfer equation can be written as: ��" = �" − �" ��" • For an isolated and homogeneous source the solution is 012 �" �" = �"(1 − � ) • When �" ≫ 1, the source is optically thick and �" ≈ �" • When �" ≪ 1, the source is optically thin and �" ≈ �"�" Brightness Temperature • While specific intensity can be expressed in units Planck Function of Jy/beam or SFU/beam, a simple and intuitive alternative is brightness temperature, which has units of Kelvin. Brightness Temperature Note that at radio wavelengths hn hn hv / kT << 1 ® ehn / kT -1»1+ -1= kT kT The Planckian then simplifies to the Rayleigh-Jeans Law. 2hn 3 1 2n 2 B (T) = » kT n c2 ehn / kT -1 c2 It is useful to now introduce the concept of brightness temperature TB, which is defined by 2n 2 I = B (T ) = kT n n B c2 B Rewriting the Radiative Transfer Equation • Similarly, we define the effective temperature as 7"8 � = �� " 98 <== • Using our definitions of brightness temperature and effective temperature, the transfer equation can be rewritten ��> = −�> + �<== ��" • Optically thick source, �" ≫ 1, �> ≈ �<== • Optically thin source, �" ≪ 1, �> ≈ �"�<== Relevant Radio Emission Mechanisms: An Introduction Bremsstrahlung Gyromagnetic Radiation Plasma Radiation − − e− e e γ γ Nucleus γ B Bremsstrahlung Radiation • Acceleration experienced in the Coulomb field − • At radio wavelengths, thermal e bremsstrahlung radiation is from γ virtually everywhere: quiet Sun, active regions, flares, and CMEs Nucleus • Nonthermal bremsstrahlung is relevant to X-ray and gamma-ray emission from flares Gyromagnetic radiation • Acceleration experienced in the magnetic field • Gyroresonance radiation from thermal electrons. Relevant in places with strong B field: e.g., active regions e− • Gyrosynchrotron radiation from relativistic γ electrons. Relevant when high energy electrons are present: e.g., flares and CMEs • Electron gyrofrequency: one “natural frequency” of the solar corona B <> �9< = ≈ 2.8� MHz 7@AB9 Plasma Radiation • Plasma oscillation, also known as “Langmuir wave”, occurs near the plasma frequency, another important natural frequency in the solar corona K 7 �<� K �G< = ≈ 8980 �< Hz ��< • Plasma radiation arises when Langmuir waves are converted to (transverse) electromagnetic waves via wave-wave interactions. 1 29:129 – Plasma Oscillations— An application of electrostatics and classical mechanics We consider a gas of electrons and positive ions (plasma). The plasma is overall neutral, i.e., the number density of the electrons and ions are the same. We think of the plasma as two interpenetratinglet’s do some derivation fluids — an negative electron fluid and a positive ion fluid.… Plasma � � x x • Electric Coulomb force acts as the restoring force Schematic diagram of the plasma, with theK Small volume of plasma in which the inset• Gauss’s Law: showing a� Stypical� = 4�� volume. Integral form within ∯theK � S �X�� Electrons= 4�� are displaced to the right plasma with equal densities of positive ions by an amount x, while the ions are and electrons.Z@[ Z@]\^ fixed. • So � = = = 4��� � \ \ < Under normal conditions,`8 there^ are always equal numbers positive ions and electrons in any • Newton’s 2nd law: � = −�� = −4�� �7�, which has volume of the plasma, so the< ` acharge8 density = 0,< and there is no large scale electric field in the plasma. Now imagine that all of the electrons are displaced to the right by a small amount x, the form of a simple harmonic oscillator: while the positive ions are held fixed, as shown on the right side of the figure above. 7 �̈ + �G<� = 0, The displacement of the electrons to the right leaves an excess of positive charge on the left side of the plasma slab and8 an excess of negative charge on the right side, as indicated by the K Z@eB< dashedwhere rectangular�G< = boxes. The= positive2��G< is the plasma frequency slab on the left and the negative slab on the right produce an electric field pointingAB toward the right that pulls the electrons back toward their original locations. However, the electric force on the electrons causes them to accelerate and gain kinetic energy, so they will overshoot their original positions. This situation is similar to a mass on a horizontal frictionless surface connected to a horizontal spring. The spring provides a restoring force that always acts to bring the mass back to its equilibrium position, thus producing simple harmonic motion. In the present problem, the electrons execute simple harmonic motion at a frequency that is called the electron plasma frequency, f pe pe 2 , where pe is the angular plasma frequency. We can apply what we know from electrostatics to compute the electric field that acts on the electrons, and use this in Newton’s second law to obtain pe . Let ne be the number density (in m3) of the electrons in the plasma, each having a charge of magnitude e. We can think of the positive region on the left side and the negative region on the right side as Plasma frequency: typical values Listen to plasma oscillations when Voyager enters the local ISM -3 Plasma �< (cm ) �G< (MHz) Environment ISM 0.05 0.003 Ionosphere 10f 3 Low corona 10hi 900 Copper 107j 2.8×10l Radio Observations in General Thermal • Emission Mechanisms Non-Thermal Chromosphere (~100 GHz) • Range of Observations Aurora (KHz) • Types of radio data Type III’s followed by Type II (45 mins) + Nobeyama Radioheliograph 17 GHz Solar radio bursts types from 1960s • Type I: short duration,