OUTLINE
IMPORTANT REVIEW PAPERS
- Stellar Radio Astronomy: Probing Stellar Atmospheres from Protostars to Giants Manuel Guedel ARAA 40, 217 (2002).
- Radio Emission from Stars George Dulk ARAA 23, 169 (1985).
- Radio Astronomy in Allen's Astrophysical Quantities, A.N. Cox Editor (2000).
- Steady Radio Emission from Stars: Observations and Emission Processes Jeffrey Linsky in Radio Emission from the Stars and the Sun, ASP Conference Series Vol. 93, 439 (1996).
- Radio Flares on Stars: Possible Solar Analogs, Tim Bastian, in Radio Emission from the Stars and the Sun, ASP Conference Series Vol. 93, 447 (1996).
TERMINOLOGY AND UNITS
- Conversion of frequencies to wavelengths:
300 GHz = 1 mm
30 GHz = 1 cm
1 GHz = 30 cm.- Unit of spectral flux density: 1 Jansky = 10^{-26} W m^{-2} Hz^{-1} =
10^{-23} ergs cm^{-2} s^{-1} Hz^{-1}.- Planck function: B_{\nu} = (2 h \nu^3/c^2) / [exp^{h \nu/kT} -1].
- In radio astronomy the Rayleigh-Jeans approximation is generally valid,
h\nu << kT_{eff} or \nu << 10^{10}T_{eff},
so exp^{h\nu/kT} = 1 + h\nu/kT and
B_{\nu} = 2 kT_{eff} \lambda^{-2}.- Thus the emission is proportional to the first power of some kind of temperature
(thermal or nonthermal equivalent at that frequency).- T_{eff} = temperature of a thermal plasma or the temperature of an optically thick blackbody that emits the same intrinsic flux at a given frequency.
- T_b = brightness temperature. Same as T_{eff} for an optically thick radiator or T_{eff} times the optical depth if optically thin.
- Note that T_{eff} and T_b and L_r(\nu) are independent of the distance to the source.
- The spectral flux density (S_{\nu}) is the observed flux from a source per Hz. \Omega is the solid angle of the source if not resolved by the telescope,
S_{\nu} = 2kT_b \lambda^{-2} \Omega Jy- L_r(\nu) = radio luminosity in ergs s^{-1} Hz^{-1}
- L_r(\nu) = 4 \pi d^2 S_{\nu}.
- L_r(\lambda) = 1.3 10^6 (6 cm/\lambda)^2 (R_{source}/R_{sun})^2 T_b
- Thus the radio luminosity can be large because either
(1) T_b is large (e.g., gyrosynchrotron or maser emission) or
(2) the emitting region is large (e.g., O star winds).- Relativistic electrons usually obey a power law distribution: n(\epsilon) ~ \epsilon^{-\delta}
\epsilon is the electron kinetic energy.
RADIATION MECHANISMS (see Gudel p 219 - 224)
- Bremsstrahlung (thermal free-free): T_b = 10^3 to few x 10^6 K,
Emission is usually unpolarized
S_{\nu} ~ \nu^2 and T_b = constant if optically thick
S_{\nu} independent of \nu and T_b ~ \nu^{-2} if optically thin
Examples: chromosphere of the Sun,
coronae of inactive stars like the Sun and Procyon, and
winds of cool giants and O stars.- Gyroresonance emission (thermal electrons in a magnetic field):
T_b = 10^7 to 10^8 K (s = 1-10).
Emission is in lines at mutiples of the gyrofrequency, but if the magnetic field is inhomogeneous (e.g., diverges with height in a stellar corona), then the lines merge into a near continuum.
Emission can be polarized because the x-mode and o-mode have different optical depths (see Dulk p. 178).
Examples: corona above sunspots, and
coronae of inactive stars like Procyon and UV Ceti at quiescence.- Gyrosynchrotron emission by thermal (T_b = 10^8 to 10^9 K) electrons
or a power law distribution of mildly relativistic electrons in a magnetic field
(s = 10-100).
S_{\nu} ~ \nu^2 and T_b = constant until the source becomes optically thin.
S_{\nu} and T_b both decrease very rapidly with increasing \nu when optically thin. (A usefully measure of the electron energies).
Emission is usually circularly polarized.
Examples: coronae of active stars including M dwarfs, RS CVn binaries, Algol binaries,
winds of O-type stars, and
some flares of active stars.- Synchrotron emission from highly relativistic electrons (T_b < 10^12 K
and s >> 100)
Note: as the electrons become more energetic, their emission becomes very bright
Emission is usually linearly polarized.
S_{\nu} ~ \nu^{5/2} when optically thick.
S_{\nu} ~ \nu^{\alpha}, where \alpha = -(\delta -1)/2 when optically thin.
Note the NEGATIVE SPECTRAL INDEX. Example: flares on M stars and active binaries.- Coherent emission (masers or plasma radiation) (T_b > 10^12 K).
Plasma emission at the fundamental or second harmonic of the plasma frequency (~9000 n_e^{0.5} Hz).
Electron cyclotron maser emission at the fundamental or second harmonic of the gyrofrequency frequency (s = 1 or 3).
Examples: flares in M dwarfs,
Type III solar bursts, and
solar millisecond spike bursts (cyclotron maser instability).
RADIO OBSERVATIONS ACROSS THE HERTZSPRUNG-RUSSELL DIAGRAM (Gudel p. C-1)
O stars, early B stars, and WR stars:
- Strong fully-ionized winds emit thermal free-free radiation.
- For optically thick winds (the usual case),
S_{\nu}~ (mass loss rate)^{4/3} \nu^{0.6}.- Note the 0.6 power law for the frequency and the dependence on the mass loss rate. So radio emission can measure the stellar mass loss rate.
- Exact formula in Gudel p. 224.
- log L_r(\nu) = 17-19.
- Emitting regions can be very large (hundreds of times the stellar radius) and can be resolved by the VLA in A Array.
- Sharp decline in the wind emission in the B stars with decreasing stellar temperature.
- Some of these stars are nonthermal sources (synchrotron emission from electrons accelerated in shocks far from the star or colliding wind shocks in binary systems).
Bp and Ap stars:
- Chemically peculiar stars of all types have very strong photospheric magnetic fields. Babcock's star has a 17 kG photospheric magnetic field.
- Typically see gyrosynchrotron emission with log L_r(\nu) = 15-18 and circular polarization.
- T_b = 10^8 to 10^9 K.
- Wind-driven magnetospheric emission model (Gudel p. 238) (Linsky, Drake, and Bastian ApJ 393, 341 (1992)).
A stars on the MS: No detections presumably because no strong magnetic fields or strong winds.
F, G, and K stars on the MS:
- Very few detections because the main sequence stars are faint emitters.
- At cm wavelengths thermal emission is detected from the solar chromosphere.
- Above sunspots gyroresonance emission at s = 1-4 is detected.
- During solar flares one sees gyrosynchrotron emission and several types of coherent emission.
- Procyon (F5 IV_V, d= 3.5 pc) shows weak gyroresonace emission.
M stars on the MS:
- Gyroresonace emission detected from UV Ceti when very inactive.
- M dwarfs have strong radio flares and emission between the obvious flares could be continuous microflaring.
- During flares M dwarfs are either strong synchrotron emitters or coherent emitters.
- Gyrosynchrotron emission accurs at the very beginning of the flare and can last for minutes to hours (Gudel p. 230) (long decay time for the relativistic electrons).
Brown dwarfs
- Old brown dwarfs not detected presumably because convection ceases or very weak after deuterium burning stops.
- LP944-20 (500 My brown dwarf) detected as a flaring and quiescent synchrotron emitter (Berger et al. Nature 410, 338 (2001)). X-ray flare also seen.
- Evidence that brown dwarfs can have magnetic fields.
- Jupiter also a strong radio source (cyclotron maser).
RS CVn, W UMa, Algol, and other short period binaries:
- Luminous gyrosynchrotron radio sources with log L_r(\nu) = 16-17.
- Detections during and outside of flares.
- Brightest emission seen at S_{\nu} = 1.1 Jy during a flare on HR 1099.
- Radio flares can last for many days. Initially the electrons are very energetic in a small core, but with time the source expands to the size of the binary system and the electrons less energetic.
- VLBA image of Algol during a flare (Gudel p. 237).
PMS stars
- PMS stars are often strong radio sources (log L_r(\nu) > 15).
- Class I objects are often thermal sources with emission from a collimated wind or jet.
- Detection of circular polarization, variability, and negative spectral indecies show that T Tau and other PMS stars are gyrosynchrotron sources. (Gudel p. 247)
- Class 0 objects are thermal wind sources and circumstellar disk sources (mm and sub-mm) emission from cold dust (T~20 K). These will likely be strong sources for ALMA.
- log L_r(\nu) decreases from 18 (Class I objects) to 15 (rapidly rotationg stars at age 10 My approaching the MS).
K and M giants and supergiants (single or widely-separated binaries):
- Thermal free-free wind emission. No magnetic emission detected so far.
- L_r is large because a large emitting volume even though T_b is small.
- Radio variability may indicate an inhomogeneous wind due to a few convective cells or variable ionization.
- Radio emission a good indicator of the stellar mass loss rate.
MAJOR RADIO OBSERVATORIES
- Main website for NRAO and the VLA
- Astronomer's research website for NRAO and the VLA.
- The Very Large Array (VLA) is an array of 27 telescopes (each 25m diameter) located west of Socorro New Mexico. VLA site map
- A Array (36 km baseline) to D array (1 km baseline). Addition of Pie Town antenna increases the baseline. There are hybrid arrays.
- Highest resolution 0.04 arcseconds.
- Receivers for 8 passbands from 74 MHz (400 cm) to 45 GHz (7 mm). The VLA is most sensitive at 3.6 cm.
- Can be used as an interferometer or as a phased array (like one telescope) as a part of VLBI observing.
- Sensitivity in various bands.
- Archive for the VLA, VLBA, and GBT. The Advanced Query Tool will tell you what observations have been made of a specific target. Then request that the appropriate files be placed in an accessable location (this may take time).
- The VLA is now being upgraded to the EVLA with all key observational parameters being improved by a factor of 10 (baselines, blandpasses, angular resolution, time resolution, etc.)
- Very Large Baseline Interferometry (VLBI) refers to the use of two or more widely separated radio telescopes for which the data are correlated after the fact using the clocks on the telescopes for the relative time signals. Time can be requested for a variety of VLBI groups of telescopes by writing a proposal to NRAO or Effelsberg.
- The Very Long baseline Array (VLBA) is a dedicated VLBI array in the US.
- 10 antennas (each 25m diameter) located between the Carribean and Hawaii.
- Maximum baseline 8611 km.
- Best resolution 0.17 mas at 7 mm.
- Passbands 7 mm to 90 cm.
- Atacamba Large Millimeter Array (ALMA)
- ALMA is a new international radio astronomy facility being built in northern Chile at an altitude of 5,000 m.
- It will operate at mm and sub-mm wavelengths.
- Report of the Sun and Stars Working Group concerning the science that could be done with ALMA.
- Effelsberg
- Green Bank Telescope (GBT)
- Aricebo
AIPS and AIPS++
- Astronomical Image Processing System (AIPS).
- Main website for AIPS
- The new 31DEC04 version is on one of the department computers for a few weeks time.
- Look at the "Cookbook" to get an overall view of what AIPS can accomplish.
- AIPS allows you to calibrate the two-dimensional Fourier transform data that comes from a radio interferometer into a two-dimensional image. This involves calibration, cleaning by removing bad telescope data, making images, and displaying the data.
- The main issue is that some receivers can accumulate phase errors between observations of quasar phase calibrators. So it is best to find and delete such data before making an image. This is an art rather than a science.
- AIPS can calibrate and make images for all VLBI observations.
- AIPS++ is a more modern package for radio astronomy image processing being constructed by an international consortium basec on C++. Not yet fully stable but usable.
PROBLEMS FOR THE STUDENTS
