Cosmic Rays and Magnetic Fields in the ISM

Transcription

1 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

2 COSMIC RAYS DISCOVERY Part 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 radioactivity Wulf (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 increase Hess & 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.

3 Role in Physics and Astrophysics Anderson discovered the positron in 1932 and shared the Nobel Prize with Hess in 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, > ev, is very much greater than available with accelerators.

4 Remarkable Cosmic Ray Spectrum from ev Power law defined from ev steepens at the knee and recovers beyond the ankle. The puzzle of ultra highenergy CRs is that they can t be confined by the Galactic B-field, they can t be produced by SNe, and they can t come from very large distances because they interact with CMB photons. knee ankle GZK limit

5 Observed Properties From observations above the atmosphere using balloons, rockets, satellites we know the following: 1. high degree of isotropy 2. power law spectra from 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 10 Be (half-life 1.5 Myr) 6. significant pressure: ~10-12 dynes cm -2 *Illustrated below with figures

6 Cosmic Ray Spectra Simpson, ARNS Intensity vs. energy per nucleon from Mev/A. The units of intensity are: particles per (m 2 s MeV/nucleon). The proton slope is I p ( E) = ( E ) GeV cm -2 s -1 sr -1 GeV -1

7 Cosmic Ray Abundances The large excesses are mainly due to spallation reactions of protons with abundant nuclei that produce elements ordinarily produced in stars at low abundances.

8 Solar modulation With 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.

9 Termination shock at 94 AU Stone et al 2005

10 Gyrofrequency w B = eb/gmc Cosmic Rays in Magnetic Fields Gyroradius r B = p^c/eb = 3.3 x E(GeV)/B -6 fi CR well-coupled to B Interaction of CR with magnetic field complex: cm for ER protons Mirroring in regions of variable field strength Field line wandering Streaming CR excite instabilities, reducing anisotropy

11 COSMIC RAY HEATING AND IONIZATION Coulomb scattering of protons on electrons, bound or free Minimum impact parameter sets scale of interaction: gm e v 2 ~ Ze 2 /r min fi s ~ pr 2 min ~ Z 2 e 4 /(gm e v 2 ) 2 ~ cm 2 = 1 barn for gv ~ c Energy transfer at r min is a maximum: DE ~ g 2 m e v 2 Rate of energy loss to electrons: de/dt = n s v DE ~ Z 2 e 4 /m e v 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 G = 3.4 z primary ev s -1 H -1 Cosmic rays in HII lose more energy since minimum energy loss less Nuclear interactions: s ~ 0.01 barn, corresponding to column ~ 100 g cm -2

12 Cosmic Ray Ionization Rate Webber (ApJ ) used satellite observations out to 42 AU (c. 1987). Estimated interstellar ionization rate: protons + heavier CR (~0.8 x protons) + electron CR (~ protons) + secondaries (5/3) z CR = (5/3) 4p j CR s de 3-4 x s -1 H -1

13 INTERSTELLAR MAGNETIC FIELDS -Synchrotron radiation -Faraday rotation -Zeeman splitting -Polarization

14 History Probably started in 1949 with the discovery of the polarization of starlight by interstellar dust. Quickly followed by the suggestion (Shklovsky1953) that synchrotron radiation emission powered the Crab Nebula. The optical polarization was confirmed the following year by Russian astronomers. Searches for the Zeeman splitting of the 21-cm line were suggested by Bolton & Wild in After 50 years of study, measuring the interstellar magnetic field remains an important challenge to observational astronomy.

15 Synchrotron Radiation Relativistic electrons gyrating in magnetic field radiate power P = 2e 2 a 2 /3c 3 = (2e 2 /3c 3 )(egvxb/m e c) 2 = 2s T c g 2 b 2 (B^2/8p) where ^ is perpendicular to v and \ k Frequency: beaming plus Doppler boosting fi n ~ g x g 2 w B^ = g 2 e B^/m e c = 4.15 x 10 6 g 2 B^ Hz Emission by power-law distribution of relativistic electrons J CR = KE -p j n µ K B^a+1 n -a where a = (p-1)/2 Observe a ~ 0.8 fi I n µ < B^1.8 > for constant J CR I n µ < B^3+a > for minimum energy Synchrotron emission is linearly polarized, up to 75% for uniform B

16 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 M51 and NGC 891 (figures below). The magnitude of the field cannot be determined without making assumptions about the electron density since the flux is proportional to B 1+a J CR. For minimum energy, the inferred local field is 6 ± 2 mg with B uniform /B tot = 0.6 (Beck 2001). Not clear whether this is rms field or <B 3.8 > 1/3.8

17 Neininger, A&A cm observations of polarized emission from the face-on galaxy M51. The magnetic field directions follow the spiral arms.

18 Synchrotron emission at 6 cm from edge-on galaxy NGC 891 showing halo emission. Sukumer & Allen ApJ Magnetic fields as well as cosmic rays must extend above the disk of the galaxy.

19 FARADAY ROTATION In 1845 Faraday discovered that the polarization of an EM wave can change in a magnetic field. Right and left circularly polarized light have different phase velocities in ionized medium: (c/v f ) 2 = 1 - (w/ w pl ) 2 (1 ± w B / w) -1, where w pl is the plasma frequency For w >> w pl, w B, the difference in phase velocities is v f- - v f+ c w pl 2 w B /w 3 µ n e B A linearly polarized wave can be decomposed into right and left circularly polarized waves. The plane of polarization rotates by ϖ when the phase difference amounts to 2 ϖ. If y is the angle representing the plane of polarization, y = (1/2)(2 ϖ/l) v f t Æ (ϖ/l) (c w pl 2 w B /w 3 ) dt

20 Hence 3 e 2 y = 2p l RM, RM Ú ds neb ª L < ne >< B 4 m c e > = 0.81 n e <B -6 > L pc where RM is the Faraday Rotation Measure. In practice, we cannot measure absolute phases (since we do not know the polarization produced by the source). Instead the wavelength dependence is used, on the assumption that the initial polarization is independent of wavelength. RMs are measured towards both extragalactic radio sources and 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, B r ~ 5 mg.

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

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

23 Extragalactic RMs: closed circles > 0 open circles < 0 R Beck SSR RMs can also be measured against extragalactic sources, but are more complicated to interpret because of the long lines of sight and contamination from the sources. The results indicate that the magnetic field has a substantial random component, especially above the plane.

24 Zeeman Measurements at 21 cm Proposed by Bolton & Wild: ApJ in a short ApJ Note Useful detailed discussion: Crutcher et al. ApJ OH for molecular clouds, e.g., Crutcher & Troland ApJ 537 L Review: see Sec. 3 of Crutcher, Heiles, & Troland Springer LNP

25 Physical Basis for Using the Zeeman Effect Add the Zeeman splitting to the ground levels of HI: E Z s ϖ s M=1 M=0 (F+1) M=-1 M=0 (F=0) For the magnetic fields of interest, the E is Z = eh 2m c negligiblecompared to the broadening of e Zeeman splitting B = MHz the basic hfs splitting (1420 MHz). Ê Á Ë B G ˆ Observing along the field, one sees only circular polarization (M=1 to 0 & M= -1 to 0). Perpendicular to the field, one sees plane polarization (ϖ parallel to the field and s perpendicular to the field).

26 Notes on the Stokes Parameters From 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.

27 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 intensity difference between the line wings. This difference (Stokes parameter V) is related to the derivative of the unpolarized intensity I, V = di dn n Z cosj where n Z µb is the Zeeman frequency and q is the angle between B and the line of sight.

28 By measuring both V and di/dn, the parallel component of the magnetic field can be measured Example comparing the Stokes V spectrum with the derivative of the unpolarized intensity. I Crutcher & Troland ApJ 537 L OH in the core of L1544

29 Results of 21-cm Zeeman Measurements Results for the diffuse CNM* (Heiles, Crutcher, & Troland 2003) There is a lot of scatter. Non detections are not shown. B eq = 0.4n HI 1/2 v. The average field is B = 5 µg. *Results for dark cloud & cores will be discussed later

30 Polarization of Starlight B _ for ~ 10 4 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.

31 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 also depend on the sampling (averaging) volume. For the Milky Way, the field is mainly parallel to the disk midplane, concentrated in the spiral arms with inter-arm reversals, and twice as large as the older value of 3 mg. The random and uniform components are the same order of magnitude. A rough value for the total field in the solar neighborhood is 6 mg (or a little less). The field increases with decreasing galactic radius, and is about 10 mg at R = 3 kpc.

32 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-arm reversals. Typical field values are 10 mg, not all that different than the Milky Way. For more on magnetic fields in external galaxies, see: R. Beck, SSR or astro-ph/

33 Midplane Pressure References: McKee in Evolution of the ISM (ASP 1990), p. 3 Boulares & Cox, ApJ (BC) It is generally assumed that, despite tremendous dynamic 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 vertically stratified and satisfies the usual equation dp dz = -r( z) g( z) where g(z) is the gravitational acceleration, mainly due to stars.

34 Hydrostatic Equilibrium (cont d) The solution is that the pressure = weight of material above: p( z) = dz' r( z') g( z') Ú z 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 consistent with what we know about the pressure contributions: p = ( p + p + p th + pturb + pram) For example, the main gas contributions included by BC are given on the next page. mag CR

35 Simplified Boulares & Cox Model Phase Density (cm -3 ) Scale height (pc) H CNM WNM WIM The total half-column of gas is about 5x10 20 cm -2, which corresponds to a (half) surface density of 6 M Sun pc -2, cool and the warm contributing roughly equal amounts.

36 Boulares-Cox Midplane Pressure Estimate p(0) ª (3.9 ± 0.6) 10 erg cm If this came from purely gas kinetic (thermal) pressure, the nt product would be nt = p(0) / k B ª 28,000 cm The thermal pressure determined from optical & UV absorption lines is ~ 3,000 cm -3 K, ~ 10 times too small. From this, we get p mag ª p CR ª10 - which together account for half of the total. The other 40% might be turbulent pressure, a more dynamic ram pressure, or larger magnetic and/or CR pressure. Complication: random field contributes pressure B 2 /24p. 12 erg -3 cm K -3

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