Cosmic Rays and Magnetic Fields in the ISM

Cosmic rays

-Introduction and history

-Observed properties

-Ionization rate

Magnetic fields

-Synchrotron radiation

-Faraday rotation

-Zeeman splitting

-Polarization

Vertical structure of the ISM

COSMIC RAYS

DISCOVERYPart of the rise of “modern” physics: early radiation detectors(ionization chambers, electroscopes) showed a dark current in 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 Astrophysics

Anderson discovered the positron in 1932 and sharedthe Nobel Prize with Hess in 1935.

Until 1952, cosmic ray research was experimentalparticle physics. It led to many discoveries: muon,pion, and other particles. Even today the energy of thehighest energy cosmic rays, > 1020 eV, is very muchgreater than available with accelerators.

Remarkable Cosmic Ray Spectrum from 108-1021 eV

Power law defined from 1010-1015 eV steepens at 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”GZK limit

Observed PropertiesFrom observations above the atmosphere usingballoons, rockets, satellites we know 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) – 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 large excesses are mainly due to spallation reactionsof protons with abundant nuclei that produce elementsordinarily produced in stars at low abundances.

Solar modulationWith I(E) decreasing rapidly withE, it is important to understandthe low-energy behavior.

The figure shows spectra atthree levels of solar activity,indicating that the Sun itselfchanges the CR intensity.

Correcting the observedspectra for solar systemeffects, or demodulation, isrequired to deduce the CRintensity in the local ISM.

Termination shock at 94 AUStone et al 2005

Cosmic Rays in Magnetic Fields

Gyrofrequency wB = eB/gmc

Gyroradius rB = p^c/eB = 3.3 x 1012 E(GeV)/B-6 cm for ER protons

Interaction of CR with magnetic field complex:

Mirroring in regions of variable field strength

fi CR well-coupled to B

Field line wandering

Streaming CR excite instabilities, reducing anisotropy

COSMIC RAY HEATING AND IONIZATION

Coulomb scattering of protons on electrons, bound or free

Minimum impact parameter sets scale of interaction:

gmev2 ~ Ze2/rmin fi s ~ prmin2 ~ Z2e4/(gmev2)2

~ 10-24 cm2 = 1 barn for gv ~ c

Energy transfer at rmin is a maximum: DE ~ g2mev2

Rate of energy loss to electrons: dE/dt = n s v DE ~ Z2e4/mev

Nuclear interactions: s ~ 0.01 barn, corresponding to column ~ 100 g cm-2

For proton cosmic rays in HI: lose 35 eV per ionization

Secondary electrons ionize HI and excite La until E<10.2 eV;rest of energy goes into heating electrons

Cosmic rays in HII lose more energy since minimum energy loss less

G = 3.4 zprimary eV s-1 H-1

Cosmic Ray Ionization RateWebber (ApJ 506 334 1998) used satellite observations out to 42 AU (c. 1987).

Estimated interstellar ionization rate: protons + heavier CR (~0.8 xprotons) + electron CR (~ protons) + secondaries (5/3)

zCR = (5/3) ∫ 4p jCR s dE ≈ 3 - 4 x 10-17 s-1 H-1

INTERSTELLAR MAGNETICFIELDS

-Synchrotron radiation

-Faraday rotation

-Zeeman splitting

-Polarization

History• Probably started in 1949 with the discovery of thepolarization of starlight by interstellar dust.

• Quickly followed by the suggestion (Shklovsky1953)that synchrotron radiation emission powered the CrabNebula. The optical polarization was confirmed thefollowing year by Russian astronomers.

• Searches for the Zeeman splitting of the 21-cm linewere suggested by Bolton & Wild in 1957.

• After 50 years of study, measuring the interstellarmagnetic field remains an important challenge toobservational astronomy.

Synchrotron Radiation

Relativistic electrons gyrating in magnetic field radiate power

P = 2e2a2/3c3 = (2e2/3c3)(egvxB/mec)2

= 2sTc g2 b2 (B^2/8p) where ^ is perpendicular to v and \ k

Frequency: beaming plus Doppler boosting fi

n ~ g x g2 wB^ = g2e B^/mec = 4.15 x 106 g2 B^ Hz

Emission by power-law distribution of relativistic electrons JCR = KE-p

jn µ K B^a+1 n-a where a = (p-1)/2

Observe a ~ 0.8 fi In µ < B^1.8> for constant JCR

In µ < B^3+a> for minimum energy

Synchrotron emission is linearly polarized, up to 75% for uniform B

Results of Synchrotron Observations

• The characteristics of synchrotron radiation, polarization and power-law spectra, are observed towards extragalactic radio sources as well as pulsars.

• They are particularly useful in tracing the direction of the magnetic fields in external galaxies, as illustrated for M51and NGC 891 (figures below).

• The magnitude of the field cannot be determined withoutmaking assumptions about the electron density since the flux is proportional to B1+a JCR. For minimum energy, the inferredlocal field is 6 ± 2 mG with Buniform/Btot = 0.6 (Beck 2001).Not clear whether this is rms field or <B3.8>1/3.8

2.8 cm observationsof polarized emissionfrom the face-on galaxyM51. The magnetic fielddirections follow thespiral arms.

Neininger, A&A 263 30 1993

Synchrotron emission at 6 cmfrom edge-on galaxy NGC 891showing halo emission.

Sukumer & AllenApJ 382 100 1991

Magnetic fields as well as cosmic rays must extendabove the disk of the galaxy.

FARADAY ROTATION

In 1845 Faraday discovered that the polarization of an EM wave canchange in a magnetic field.

Right and left circularly polarized light have different phasevelocities in ionized medium:

(c/vf)2 = 1 - (w/ wpl)2(1 ± wB/ w)-1, where wpl is the plasma frequency

For w >> wpl , wB , the difference in phase velocities is

vf- - vf+ ≈ c wpl2 wB /w3 µ neB

A linearly polarized wave can be decomposed into right and leftcircularly polarized waves. The plane of polarization rotates by #when the phase difference amounts to 2 #. If y is the anglerepresenting the plane of polarization,

y = (1/2)(2 #/l) ∆ vf t Æ (#/l) ∫ (c wpl2 wB /w3) dt

Hence>><<ª≡= Ú ||e||||e

24

e

3

,e

2 BnLBndsRMRMcm

lpy

where RM is the Faraday Rotation Measure. In practice, wecannot measure absolute phases (since we do not know the polarization produced by the source). Instead the wavelengthdependence is used, on the assumption that the initial polarization is independent of wavelength.

RMs are measured towards both extragalactic radio sourcesand pulsars (see the following figures).For pulsars, measurements of both RM and DM yield values of B|| for the WIM ~ 1.4 mG. Random field much larger,Br ~ 5 mG.

= 0.81 ne <B-6> Lpc

SSR 99 243 2001

Pulsar RMs within 8o of the galactic plane. positive values + negative values o

The field reversals are believed to occur in between thespiral arms. Below, the early results of Rand & Lyne (1994) are superimposed on the electron density model ofTaylor & Cordes (1993) discussed in Lecture 9

Heiles, ASP 80 497 1995

Sun

R Beck SSR 99 243 2001

Extragalactic RMs: closed circles > 0 open circles < 0

RMs can also be measured against extragalactic sources,but are more complicated to interpret because of the longlines of sight and contamination from the sources. The results indicate that the magnetic field has a substantial random component, especially above the plane.

Zeeman Measurements at 21 cm

Proposed by Bolton & Wild:ApJ 125 296 1957 in a short ApJ Note

Useful detailed discussion:Crutcher et al. ApJ 407 175 2003

OH for molecular clouds,e.g., Crutcher & TrolandApJ 537 L139 2000

Review: see Sec. 3 ofCrutcher, Heiles, & TrolandSpringer LNP 614 155 2003

Physical Basis for Using the Zeeman EffectAdd the Zeeman splitting to the ground levels of HI:

______________________________

__________

M=1M=0 (F+1)M=-1

M=0 (F=0)

s # s

EZ

MHz). (1420 splitting hfs

basic theof broadening

the tocompared negligibleis

MHz400.12

splittingZeeman theinterest,

of fields magnetic For the

Z ˜¯

ˆÁË

Ê==G

BB

cm

eE

e

h

Observing along the field, one sees only circular polarization (M=1to 0 & M= -1 to 0). Perpendicular to the field, one sees planepolarization (! parallel to the field and s perpendicular to the field).

Notes on the Stokes ParametersFrom Rybicki & Lightman, an EM wave can be expressed using either the observer’s x-y frame or the principle axes of a polarization ellipse.The angle b gives the components in the former, and c is the angle that the principle axis makes with the x-axis.

The Stokes parameters are then defined as:

Note that, in addition to the total intensity I, there are only two independent parameters: Q or U measures the direction of the linear polarization and V measures the degree of circular polarization.

Application of the 21-cm Zeeman Effect

If the 21-cm transition were not (thermally & turbulently)broadened, the polarization capability of radio receivers would resolve the Zeeman effect & measure the magnetic field.

If the field has a component along the line of sight, the broadened line wings will be circularly polarized, so the suggestion of Bolton & Wild was to compare the intensitydifference between the line wings. This difference (Stokes parameter V) is related to the derivative of the unpolarized intensity I,

Jnn

cosZd

dIV =

where nZµB is the Zeeman frequency and q is the anglebetween B and the line of sight.

By measuring both V and dI/dn, the parallel component of the magnetic field can be measured

Example comparing theStokes V spectrum withthe derivative of the un-polarized intensity.

Crutcher & TrolandApJ 537 L39 2000OH in the core of L1544

I

Results of 21-cm Zeeman MeasurementsResults for the diffuse CNM*(Heiles, Crutcher, & Troland 2003)

There is a lot of scatter. Non detections are not shown.Beq = 0.4nHI

1/2 ∆v. The average field is |B||| = 5 µG.

*Results for dark cloud & cores will be discussed later

Polarization of Starlight

B_ for ~ 104 nearby stars, c.f. magnetic alignment of dust grains(discussed in a later lecture on magnetic fields and star formation).

1. The galactic field is “mainly in the plane”.2. It is strong along the local spiral arm.3. Random component is up to 50% larger than uniform.4. Out of plane features are associated with loops & regions of star formation.

6. Summary

Different techniques measure different things, e.g., field components parallel (RM & Zeeman) and perpendicular (synchrotron and dust polarization). Zeeman measurements are sensitive to neutral regions, and synchrotron emission is particularly useful for external galaxies. The results alsodepend on the sampling (averaging) volume.

For the Milky Way, the field is mainly parallel to the diskmidplane, concentrated in the spiral arms with inter-armreversals, and twice as large as the older value of 3 mG. The random and uniform components are the same orderof magnitude. A rough value for the total field in the solarneighborhood is 6 mG (or a little less). The field increases with decreasing galactic radius, and is about 10 mG at R = 3 kpc.

Summary (concluded)

For external galaxies, the synchrotron emission studies show the effects of spiral structure, the existence of thin and thick disk components, and occasionally inter-armreversals. Typical field values are 10 mG, not all that differentthan the Milky Way.

For more on magnetic fields in external galaxies, see: R. Beck, SSR 99 243 2001 or astro-ph/0012402

Midplane Pressure References:

McKee in “Evolution of the ISM” (ASP 1990), p. 3Boulares & Cox, ApJ 365 544 1990 (BC)

It is generally assumed that, despite tremendousdynamic activity, the Milky Way is in hydrostaticequilibrium, its stability guaranteed by a large midplanepressure (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.

)()( zgzdz

dpr-=

The solution is that the pressure = weight of material above:

)'()'(')( zgzdzzpz

rÚ•

=

This requires a knowledge of both r(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 r(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 Boulares & 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( -¥±ªp

Kcm000,28/)0( 3B

-ª= 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-3 K, ~ 10 times too small. From this, 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.Complication: random field contributes pressure B2/24p.

-312CRmag cmerg10-ªª pp