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Possibility of detecting magnetic charges using pulsar emission
Volume 72A, number 2
PHYSICS LETTERS
25 June 1979
POSSIBILITY OF DETECTING MAGNETIC CHARGES USING PULSAR EMISSION W. WILSON and N.V.V.J. SWAMY’ Department of Physics, Oklahoma Stare University, Stlllwater, OK 74074, USA Received 26 March 1979 Revised manuscript received 24 April 1979
Modification of well-known plasma-wave dispersion relations due to particles bearing magnetic charge is presented. If these charges exist in the interstellar medium, the effects of the new modes they allow may be detectable in pulsar emission.
There have been several papers on magnetic poles in recent times [11 following the original work of Dirac [2] who sought to symmetrize Maxwell’s equations and explain the observed electric charge. Schwinger [3] proposed the existence of dually charged particles bearing both electric and magnetic charges in a quan-
Since the theory underlying plasma wave dispersion is well known [6] we present here the bare essentials. Maxwell’s equations with magnetic charges are nicely discussed in Schwinger’s paper. In the multicomponent fluid description [7], we assume ~ species of particles with number densities N1 N2, N,~and that a particle
tized way to explain the violation of CF invariance in
in the ath species has mass ma, electric charge ea, magnetic charge Za and velocity Va. Whenever either ea or assumes the value 0, the corresponding number density refers to singly charged particles. The hydrodyna~ mical equation ofmotion will have an additional Lorentz force termg~N~(B (V/c).X E) due to the magnetic charge g~.We linearize the equations in the usual way, separating the variables into large equilibrium values and small perturbations and consider an infinite, cold, uniform plasma E= E + K 0 2o1 = VOa e c., = VNOa = alvoalat, (1) 0 = E0 = N =0 N e~ Oa ~=
particle interactions. Magnetic chargeshave also figured in non-abelian gauge theories [4], and it is held by some that the existence of quarks almost implies the existence of magnetic charges. The recent Stanford levitation experiments [5] on the detection of fractional electric charges suggests that the search for magnetic charges should be taken seriously. The heavy mass and the strong binding of such charges (mass 137 times the mass of a typical vector boson and binding (137)2 times the force between similar electrically charged particles) have stood in the way of detection of these in the poles laboratory. While the possible detection of magnetic in elementaiy particle physics has been discussed in the literature, it is the purpose of this letter to point out that well-known plasma-wave dispersion
,
...,
—
‘
— —
1~a Oa
relations are significantly modified and new modes are generatedby particles bearing magnetic charge. Looking for these effects would be a way of detecting these charges. In particular the dispersion ofelectromagnetic pulses from pulsars would be altered if magnetic charges happen to exist in interstellar media. Research supported by the College of Arts and Sciences, Oklahoma State University.
188
The well known procedure of taking the Fourier transforms in time and space of the Maxwell equations and eliminating one of the fields leads to the dispersion relations. After Fourier transforming in time typical equations involving magnetic charges are, for instance, V B1~,,,= 4ir
E g~N~’~ a
Volume 72A, number 2
PHYSICS LETTERS
~
25 June 1979 FREQUENCY
(2)
/
a
/
\
/‘~—
The dispersion relations .are found to be
(3)
WWpHW+~)OO~
(4)
SLOPE
___~::::::~‘
~
FAST WAVE
AVE
which correspond to transverse and longitudinal modes, respectively. Here we have introduced v (e~+g~) WPH=E471 =1
ma
N0a,
(5)
WAVENUMBER k
Fig. 2. Frequency versus wavenumber for the transverse waves.
V
=
E
2 .
(4~~.)2 N~N0~
a<~1
(6)
m0 m~ (e~gp— e~g~)
As can perhaps be expected, the magnetic charge leads to a doubling of the number of plasma modes. When 4~$/o4H ~ 1, the roots of eq. (4) are to order (v~c~.oIc&pH)4
or transverse ~ ~‘pL~ The qualitative properties the modes can propagate onlyof if the ~ ~two branches are quite different. The phase velocities V~, ca/k and the group velocity V 5 d~/dkare different depending on whether c~~ (&~PHor ~ ~‘pL~ From eq. (8) we find W
‘~
Vpc(1_w~HIw2)_hI’2, ~ 2I~(1)2IcLi~’2,
(7)
WPL =
A plot of this is shown in fig. 1. Ukewise from eq. (3) we find the frequencies of the transverse waves ~ ~pH + c2k2
~ “-‘~o/(’4i~ + c2k2),
(8)
where the expansion is correct to order (~,‘~~/(‘4H + e2k2))2. This is sketched in fig. 2 and we notice that
FREQUENCY w
WPL
WAVENUMBER
k
Fig. 1. Frequency versus wavenumber for the longitudinal oscillations,
(9)
~“~
Vg = c(1 HI~2)~2’ = ~ (1 “~I~’pL)’’ ‘~‘~ ~ (10) The phase velocity at the upper branch is, thus, super—
—
luminal (V~> c) while the lower branch is subluminal (V~< c) and we distinguish the two branches as that of a fast wave and a slow wave, respectively. The group velocity is, of course, always less than c. Applying this theoiy to pulsar emission we see that when the emitted pulse has a range of frequency components, the arrival times of different frequencies at the earth will vary. The arrival time of a pulse that has traveled a distance D is DI Vg and the frequency dependence of this can be found from eq. (10) to be given by the dispersion measure (d/dw) (DI Vg)
_________
~~~pL’
c(ci)
—(D12c) ~ ~2(DIc)(c~Ic~,2),
~‘> ~pL~
(11)
Thus, for the slow transverse waves tl~elower frequency components arrive ahead of the higher frequencies! This is just the opposite of what happens in the case of the fast transverse wave, which is similar to the standard 189
Volume 72A, number 2
PHYSICS LETTERS
plasma result, where the lower frequencies lag behind the higher frequency components. If the particles in the intervening interstellar medium between the earth and a pulsar carry magnetic charges, the low frequency dispersion measure should exhibit radically different behavior than hitherto known, and it would be worth designing experiments to detect these effects. It interesting to note that the Schwinger quantization of magnetic charge differs from the Dirac quantization by a factor of 4 ~S
eg//lc = 1/2 (Dirac) = 2 (Schwinger)
.
However, a precise knowledge of the equilibrium number densities of the particles is necessary to decide between these two, even when accurate measurements of the frequencies are available. Calculations based on the kinetic theory yield the same end results with the approximations used here.
190
25 June 1979
effects of higher temperatures and collisions (if any) are currently under study. The
References Eli J.L. Newmeyer and J.S. Trefil, Phys. Lett. 38B (1972) 524; Z. Horvath and L. Palla, Phys. Lett. 69B (1977) 197; C. Montonen and D. Olive, Phys. Lett. 72B (1977) 117. [21 P.A.M. Dime, Phys. Rev. 74 (1948) 817. [31 J. Schwinger, Science 165 (1969) 757;Phys. Rev. 173 (1968) 1536. [4] P. Goddard and D.I. Olive, Rep. Prog. Phys. 41(1978) 91. [51G.S. LaRue, W.M. Fairbank and A.F. Hebard, Phys. Rev. Lett. 38(1977)1011; ,G.S. LaRue, W.M. Fairbank and J.D. Phillips, Phys. Rev. Lett. 42 (1979) 142. [6] I.B. Bernstein and S.K. Trehan, Nuci. Fusion 1 (1960) 3. [7] T.H. Stix, The theory of plasma waves (McGraw-Hill, New York, 1962).
PHYSICS LETTERS
25 June 1979
POSSIBILITY OF DETECTING MAGNETIC CHARGES USING PULSAR EMISSION W. WILSON and N.V.V.J. SWAMY’ Department of Physics, Oklahoma Stare University, Stlllwater, OK 74074, USA Received 26 March 1979 Revised manuscript received 24 April 1979
Modification of well-known plasma-wave dispersion relations due to particles bearing magnetic charge is presented. If these charges exist in the interstellar medium, the effects of the new modes they allow may be detectable in pulsar emission.
There have been several papers on magnetic poles in recent times [11 following the original work of Dirac [2] who sought to symmetrize Maxwell’s equations and explain the observed electric charge. Schwinger [3] proposed the existence of dually charged particles bearing both electric and magnetic charges in a quan-
Since the theory underlying plasma wave dispersion is well known [6] we present here the bare essentials. Maxwell’s equations with magnetic charges are nicely discussed in Schwinger’s paper. In the multicomponent fluid description [7], we assume ~ species of particles with number densities N1 N2, N,~and that a particle
tized way to explain the violation of CF invariance in
in the ath species has mass ma, electric charge ea, magnetic charge Za and velocity Va. Whenever either ea or assumes the value 0, the corresponding number density refers to singly charged particles. The hydrodyna~ mical equation ofmotion will have an additional Lorentz force termg~N~(B (V/c).X E) due to the magnetic charge g~.We linearize the equations in the usual way, separating the variables into large equilibrium values and small perturbations and consider an infinite, cold, uniform plasma E= E + K 0 2o1 = VOa e c., = VNOa = alvoalat, (1) 0 = E0 = N =0 N e~ Oa ~=
particle interactions. Magnetic chargeshave also figured in non-abelian gauge theories [4], and it is held by some that the existence of quarks almost implies the existence of magnetic charges. The recent Stanford levitation experiments [5] on the detection of fractional electric charges suggests that the search for magnetic charges should be taken seriously. The heavy mass and the strong binding of such charges (mass 137 times the mass of a typical vector boson and binding (137)2 times the force between similar electrically charged particles) have stood in the way of detection of these in the poles laboratory. While the possible detection of magnetic in elementaiy particle physics has been discussed in the literature, it is the purpose of this letter to point out that well-known plasma-wave dispersion
,
...,
—
‘
— —
1~a Oa
relations are significantly modified and new modes are generatedby particles bearing magnetic charge. Looking for these effects would be a way of detecting these charges. In particular the dispersion ofelectromagnetic pulses from pulsars would be altered if magnetic charges happen to exist in interstellar media. Research supported by the College of Arts and Sciences, Oklahoma State University.
188
The well known procedure of taking the Fourier transforms in time and space of the Maxwell equations and eliminating one of the fields leads to the dispersion relations. After Fourier transforming in time typical equations involving magnetic charges are, for instance, V B1~,,,= 4ir
E g~N~’~ a
Volume 72A, number 2
PHYSICS LETTERS
~
25 June 1979 FREQUENCY
(2)
/
a
/
\
/‘~—
The dispersion relations .are found to be
(3)
WWpHW+~)OO~
(4)
SLOPE
___~::::::~‘
~
FAST WAVE
AVE
which correspond to transverse and longitudinal modes, respectively. Here we have introduced v (e~+g~) WPH=E471 =1
ma
N0a,
(5)
WAVENUMBER k
Fig. 2. Frequency versus wavenumber for the transverse waves.
V
=
E
2 .
(4~~.)2 N~N0~
a<~1
(6)
m0 m~ (e~gp— e~g~)
As can perhaps be expected, the magnetic charge leads to a doubling of the number of plasma modes. When 4~$/o4H ~ 1, the roots of eq. (4) are to order (v~c~.oIc&pH)4
or transverse ~ ~‘pL~ The qualitative properties the modes can propagate onlyof if the ~ ~two branches are quite different. The phase velocities V~, ca/k and the group velocity V 5 d~/dkare different depending on whether c~~ (&~PHor ~ ~‘pL~ From eq. (8) we find W
‘~
Vpc(1_w~HIw2)_hI’2, ~ 2I~(1)2IcLi~’2,
(7)
WPL =
A plot of this is shown in fig. 1. Ukewise from eq. (3) we find the frequencies of the transverse waves ~ ~pH + c2k2
~ “-‘~o/(’4i~ + c2k2),
(8)
where the expansion is correct to order (~,‘~~/(‘4H + e2k2))2. This is sketched in fig. 2 and we notice that
FREQUENCY w
WPL
WAVENUMBER
k
Fig. 1. Frequency versus wavenumber for the longitudinal oscillations,
(9)
~“~
Vg = c(1 HI~2)~2’ = ~ (1 “~I~’pL)’’ ‘~‘~ ~ (10) The phase velocity at the upper branch is, thus, super—
—
luminal (V~> c) while the lower branch is subluminal (V~< c) and we distinguish the two branches as that of a fast wave and a slow wave, respectively. The group velocity is, of course, always less than c. Applying this theoiy to pulsar emission we see that when the emitted pulse has a range of frequency components, the arrival times of different frequencies at the earth will vary. The arrival time of a pulse that has traveled a distance D is DI Vg and the frequency dependence of this can be found from eq. (10) to be given by the dispersion measure (d/dw) (DI Vg)
_________
~~~pL’
c(ci)
—(D12c) ~ ~2(DIc)(c~Ic~,2),
~‘> ~pL~
(11)
Thus, for the slow transverse waves tl~elower frequency components arrive ahead of the higher frequencies! This is just the opposite of what happens in the case of the fast transverse wave, which is similar to the standard 189
Volume 72A, number 2
PHYSICS LETTERS
plasma result, where the lower frequencies lag behind the higher frequency components. If the particles in the intervening interstellar medium between the earth and a pulsar carry magnetic charges, the low frequency dispersion measure should exhibit radically different behavior than hitherto known, and it would be worth designing experiments to detect these effects. It interesting to note that the Schwinger quantization of magnetic charge differs from the Dirac quantization by a factor of 4 ~S
eg//lc = 1/2 (Dirac) = 2 (Schwinger)
.
However, a precise knowledge of the equilibrium number densities of the particles is necessary to decide between these two, even when accurate measurements of the frequencies are available. Calculations based on the kinetic theory yield the same end results with the approximations used here.
190
25 June 1979
effects of higher temperatures and collisions (if any) are currently under study. The
References Eli J.L. Newmeyer and J.S. Trefil, Phys. Lett. 38B (1972) 524; Z. Horvath and L. Palla, Phys. Lett. 69B (1977) 197; C. Montonen and D. Olive, Phys. Lett. 72B (1977) 117. [21 P.A.M. Dime, Phys. Rev. 74 (1948) 817. [31 J. Schwinger, Science 165 (1969) 757;Phys. Rev. 173 (1968) 1536. [4] P. Goddard and D.I. Olive, Rep. Prog. Phys. 41(1978) 91. [51G.S. LaRue, W.M. Fairbank and A.F. Hebard, Phys. Rev. Lett. 38(1977)1011; ,G.S. LaRue, W.M. Fairbank and J.D. Phillips, Phys. Rev. Lett. 42 (1979) 142. [6] I.B. Bernstein and S.K. Trehan, Nuci. Fusion 1 (1960) 3. [7] T.H. Stix, The theory of plasma waves (McGraw-Hill, New York, 1962).