The diffuse “warm ionized medium” (WIM): about 90% of ionized hydrogen (HII), in a warm and diffuse phase.
Visible trough its H- emission in our Galaxy.
Kinetic temperature: about K.
Mass: 30 \% of the ISM total mass.
Density: about .
Ionization fraction: .
Source of heat: ionizing photons from hot massive stars.
Unsolved problem: a homogeneous galactic HI distribution should absorbe the ionizing UV flux.
Solution: H I clouds cannot be spread evenly throughout the galaxy; large portions of the galaxy must have been cleared of H I.
Techniques used to detect the Warm Ionized Medium:
1) low frequency radio observations,
2) the dispersion of radio pulses of pulsars
3) hydrogen recombination emission.
Electromagnetic waves from pulsars interact with the free electrons in the WIM.
Consequence: time dispersion of the pulse.
The plasma frequency is given by:
Comparison with pulsar pulse.
Index of refraction of the ISM:
Difference between group velocity and phase velocity :
At high frequency in the pulse (), the term () is negligiable. Time for a pulse of frequency to arrive from a pulsar at a distance :
For the non-negligiable case, we can Taylor expand the term :
The time delay between the phase and group velocities is:
, which reads:
Define the dispersion measure .
The change in time delay with frequency is:
The dispersion measure used to determine the mean electron density in the ISM.
Application: determine electron density to the Crab pulsar.
Observed delay between pulses at frequencies 100 MHz and 400 MHz: 23.5 s.
First, we obtain the electron column density to the Crab pulsar:
Distance of the Crab Nebula: light years
The average electron density:
H-alpha Emission from the WIM
Weak H-alpha emission from the WIM.
Intensity of emission from is given by:
where is the effective recombination coefficient, at K.
The integral part of the equation above is called the emission measure, designated EM.
The emission measure is important for calculating line strengths in WIM.
We assume: .
Optical depth, .
Using the opacity for ionized hydrogen, the optical depth is:
Constant source temperature: then only the density changes along the line of sight.
is then proportional to
EM is the amount of emission and absorption along the line of site.
Particles approach each other along the line of site.
Recombination line strengths are proportional to the emission measure.
Measuring both the emission measure and the temperature of the region can be determined.
In the Milky Way: 90% of the ionized gas is in fully ionized, diffuse form.
Volume and spatial distribution.
What happens to the nearby ISM under the action of their strong UV radiation?
A blackbody with emits about 1/3 of its radiation in photons
with energy higher than 13.6 eV
Remember: eV is the ionization threshold of the hydrogen atom.
These photons can ionize a substantial fraction of the surrounding ISM.
Exercise 1: Compute the rate of Lyman continuum photons of an O5 star (assume a blackbody spectrum).
Mass: solar masses;
Effective temperature ,
Exercise 2: Compute the same quantity for the Sun.
Exercise 3: The peak emission measure in M42 is Approximate the nebula as a sphere with radius 0.3 pc. Compute the rate of H recombinations in the nebula. Assume a gas temperature , and assume singly ionized He with He/H=0.1.
Exercise 4: The mass distribution of GMCs in the Galaxy is given by
which holds for , with , and (a) Calculate the total mass in GMCs in the Galaxy. (b) Calculate the number of GMCs in the Galaxy with
Lyman continuum photons: energy larger than 13.6 eV. Compute the corresponding frequency .
The number of photons emitted in over all solid angles per unit time per unit area at the surface of the star:
The number of photons emitted by a star (per unit time) :
In the range of interest, we have:
Apptoximation of the black body curve with the the Weins approximation:
Change of variables and integration by parts:
The definite integral yields the result:
The results is:
photons per second.
For a Sun-like star (spectral type G3, effective temperature ):
the quantity is much larger:
Fraction of ionizing: 25% for an O5 star; only for a G3 star.
How many ionizing UV photons does the Sun emit?
Answer only depends on temperature and radius of the star.
The production rate for a Sun-like star is smaller by the following quantity:
Definition of the Stromgren Sphere.
Within Stromgren Sphere: ionization is maintained by absorption of ionizing photons radiated by a central hot star.
In a steady state, hydrogen recombination is balanced by photoionization.
: rate of emission of hydrogen-ionizing photons.
Equating the rates of photoionization and radiative recombination, gives the steady state condition for ionization balance:
where we used the recombination coefficient .
We assume that the hydrogen density be
M. Harwit, “Astrophysical Concepts”, Fourth Edition
B. T. Draine, “Physics of the interstellar and intergalactic medium,” Chapter 15
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