Lecture 14 Cosmic Rays
1. Introduction and history2. Locally observed properties3. Interactions4. Demodulation and ionization rate5. Midplane interstellar pressure
General ReferenceMS Longair, High Energy Astrophysics
(especially Volume I Ch. 9)
1. IntroductionDISCOVERY
Part of the rise of “modern” physics: early radiation detectors(ionization chambers, electroscopes) showed a dark currentin the absence of sources.
Rutherford (1903): most comes from radioactivityWulf (1910): dark current down by 2 at top of Eiffel Tower -
could not be gamma rays Hess (1912): 5 km open-balloon flight showed an increaseHess & Kohlhörster (by 1914): balloon flights to 9 km ...
Studies of the variation with height, latitude & longitude confirmed the particle nature of cosmic rays (Millikan’s name) originating above the Earth’s atmosphere.
Role in Physics and AstrophysicsAnderson discovered the positron in 1932 and sharedthe Nobel Prize with Hess in 1935.
Until 1952, cosmic ray research was experimental particle physics. It led to many discoveries: muon, pion, and other particles. Even today the energy of the highest energy cosmic rays, > 1020 eV, is very much greater than available with accelerators.
The extraterrestrial nature of cosmic rays might have early confronted astronomers, but this challenge could not be faced until mid 20th century. Todaycosmic rays are an important part of solar system and galactic astrophysics, including the ISM.
Remarkable Cosmic Ray Spectrum from 108-1021 eV
Power law defined from 1010-1015 eV steepensat the “knee” and recoversbeyond the “ankle”.
The puzzle of ultra high-energy CRs is that they can’t be confined by the Galactic B-field, they can’t be produced by SNe, andthey can’t come from very large distances because theyinteract with CMB photons.
“knee”
“ankle”GZKlimit
2. Locally Observed PropertiesFrom observations above the atmosphere usingballoons, rockets, satellites we know (Longair I Ch. 9) the following:
1. high degree of isotropy2. power law spectra from 109-1014 eV (and higher)*3. low-energy CRs excluded from solar system*4. (mainly) solar abundances*5. short lifetime in the Milky Way (20 Myr) – c.f.
detection of radioactive 10Be (half-life 1.5 Myr) 6. significant pressure: ~10-12 dynes cm-2
*Illustrated below with figures
Cosmic Ray SpectraSimpson, ARNS 33 330 1983
Intensity vs. energy per nucleonfrom 10 – 107 Mev/A. The units of intensity are:particles per (m2 s MeV/nucleon).
The proton slope is -2.75.
111275.23p GeVsrscm)
GeV(1067.1)( −−−−−−×=
EEI
Cosmic Ray Abundances
The excesses are largely due to spallation reactions ofprotons with abundant nuclei that can produce elements That ordinarily are produced in stars at low abundances.
The Electron Spectrum
Although similar to protons, the electrons are even morereduced in intensity at low energies. The distribution is also affected by energy loss from synchrotron emission.
3. Interactions
Energy per nucleon from 2-1000 MeV/A
Curves vary as 5/3 power
NB: The ordinate is the range multiplied by (Z2/A) for the projectile. The range of a 10-MeV proton is only ~ 1 gr cm-2
Most CRs have E ~ 1 GeV. They interact primarily with atomic electrons,exciting & ionizing atoms, as is well known from experiment (see figure) and from Bethe’s theory.
Range-Energy Relation
Nuclear and Magnetic Interactions
At GeV energies, the nuclear cross section is ~ 10 mb, equivalent to ~ 100 gr cm-2, thus nuclear are less important than electronic interactions.
But scattering from bent or kinked magnetic field lines can be more important. It arises from the inability of a charged particle to continue spiraling around a magnetic field when the fields vary rapidly in space. Another important CR interaction is with Alfven waves. These magnetic processes are especially important where the interstellar turbulence is MHD in nature. The affect the transport of CRs through the galaxy.
4. DemodulationWith I(E) decreasing rapidly with E, it is important to understand the low-energy behavior.
The figure shows spectra at three levels of solar activity, indicating that the Sun itself changes the CR intensity.
Correcting the observed spectra for solar system effects, or demodulation, is required to deduce the CR intensity in the local ISM.
Effects of the Earth’s Magnetic Field
The effects of the Earth’s magnetic field have been studied extensively for more than 100 years and are reasonably well understood. Satellite observations of CRs extend beyond this region.
Interfaces in the Heliosphere
Terminal shock c.f. solar wind
Suess, Rev Geophys 28 1 1990
Bow shock c.f.interstellar “wind”
Deducing the demodulated (or true) CR intensity makesuse of satellite observations as a function of heliocentricdistance and transport theory. The satellite observationsare now approaching the crucial terminal shock region.
Satellite Locations vs. Time
Cosmic Ray Ionization Rate
2heavy35
sec
psecheavyCR
≅≅
=
ff
ff ζζ
Given a demodulated CR intensity, the ionization rate can be calculated by integration with the ionization cross section.H, He, and H2 are the most important targets. A basic fact isthat 37 eV is needed to make an ion pair, so a 2 MeV protonmakes about 54,000 ions. The CR ionization rate per proton is
Integrating down to 2 MeV, Spitzer & Tomasko (ApJ 152 971 1969) found:
117CR
118p s102ands106 −−−− ×≈×≈ ζζ
With a 1975 demodulation, the rate increases to ςCR = 5x10-17 s-1
Cosmic Ray Ionization Rate UpdateWebber (ApJ 506 334 1998) used satellite observations out to 42 AU (c. 1987).
Repeating the demodulation calculations, the ionization rate down to 10 MeV/nucleon is
Going down to 2 MeV would increase this by ~ 50%.
117CR s10)43( −−×−=ζ
5. Midplane PressureReferences:
McKee in “Evolution of the ISM” (ASP 1990), p. 3Boulares & Cox, ApJ 365 544 1990 (BC)
It is generally assumed that, despite itremendousdynamic activity, the Milky Way is in hydrostatic equilibrium, its stability guaranteed by a large midplane pressure (from several components) and by a large halo.
For simplicity, we assume that the ISM is verticallystratified and satisfies the usual equation
where g(z) is the gravitational acceleration, mainlydue to stars.
)()( zgzdzdp ρ−=
The solution)'()'(')( zgzdzzp
z
ρ∫∞
=
requires a knowledge of both ρ(z) and g(z). We know that the former is very uncertain, but the latter is also uncertain by 25-35%. McKee and BC make estimates of the contributions to ρ(z) of the observed phases to estimate p(0). Then they see whether the result is consistentwith what we know about the pressure contributions:
CRmagramturbth )( pppppp ++++=
For example, the main gas contributions included by BC are given on the next page.
Hydrostatic Equilibrium (cont’d)
15000.025WIM
4000.1WNM
1350.3CNM
700.6H2
Scale height (pc)Density (cm-3)Phase
Simplified Boulare & Cox Model
The total half-column of gas is about 5x1020 cm-2, which corresponds to a (half) surface density of 6 MSun pc-2,cool and the warm contributing roughly equal amounts.
Boulares-Cox Midplane Pressure Estimate-312 cmerg10)6.09.3()0( −×±≈p
Kcm000,28/)0( 3B
−≈= kpnT
If this came from purely gas kinetic (thermal) pressure, the nT product would be
The thermal pressure determined from optical & UV absorption lines is ~ 3,000 cm-3K, ~ 10 times too small. From this and the precious lecture, we get
which together account for half of the total. The other40% might be turbulent pressure, a more dynamic ram pressure, or larger magnetic and/or CR pressure.
-312CRmag cmerg10−≈≈ pp
