Cosmic rays and climate change over the past 1000 million years
aa r X i v : . [ a s t r o - ph . S R ] M a r Title of paper “COSMIC RAYS AND CLIMATE CHANGE OVER THE PAST 1000 MIL-LION YEARS”by T. Sloan (corresponding author)Dept of Physics,Lancaster University,Lancaster LA1 4YB,UK.email [email protected] number (44)(0)17687 74467Fax number (44)(0)1524 844037Second author,A.W. Wolfendale,Dept of Physics,Durham University,Rochester Building,South Road,Durham DH1 3LE,UK.email [email protected] 1
OSMIC RAYS AND CLIMATE CHANGE OVER THEPAST 1000 MILLION YEARS
T. Sloan, (Dept of Physics, University of Lancaster) A.W. Wolfendale, (Dept. of Physics, University of Durham)
Abstract
The Galactic cosmic ray (GCR) intensity has been postulated by others to vary cyclicallywith a peak to valley ratio of ∼ The rate of variation of the GCR intensity over the last 1000 million years (Ma) was investigatedby Shaviv (Shaviv 2003). He deduced from a model that the GCR intensity varies by a factor ∼ Corresponding author: email [email protected] ∼ The conventional picture of our Galaxy, the Milky Way, (and many other galaxies) is that it hasspiral arms, these being regions where new star formation mainly takes place. In turn, shortlived massive stars which later explode to form Type 2 Supernovae (SN), are mainly found inthe Arms. Such SN remnants are generally thought to be responsible for the production of GCRwith a differential injection energy spectrum falling as E − n , with spectral exponent n ≃ E ∼ eV. The current view is that the extra star formation is caused by theincreased gas pressure in the Arms from the spiral density wave. In the present vicinity of theSolar System, the centre lines of the SA are separated by about 1.7 kpc between the Local Armand the neighbouring Sagittarius-Carina arm (Gies and Helsel, 2005 and Vall´ee 2005).Separations between the SA nearer the Galactic Centre and in the far Outer Galaxy varysomewhat in the range 1.7 to 3 kpc. The variability arises from the inevitability of a non-perfectspiral wave, the gas density being non-uniform in the pre-Galactic environment, together withtidal shear from other galaxies. The adopted form of the Spiral Arms at present comes fromoptical and radio measurements of stars and gas as a function of Galactic longitude and latitude.Examining the distributions of the positions of SN remnants shows that they are roughlydistributed about the the centre lines of the SA as Gaussian shapes with probable long tails.Such long tails will reinforce our conclusions of a small difference in the Galactic GCR intensitybetween the IA and SA. However, we make the conservative assumption of a Gaussian shape inwhat follows. The spatial distribution of Type 2 SN has been determined (Bartunov et al., 1994)to have a half-width at half maximum of ∼ ∼ .2 Model predictions for the ratio of the IA and SA GCR intensities. To a first approximation one can assume that GCR are produced randomly in time and space inthe SA but modulated by the radial distribution described in section 2.1. The GCR then diffusewith a spatially independent diffusion coefficient. Such a model is that used previously by us(eg Erlykin and Wolfendale, 2003), although without an SA/IA modulation. In that work a GCRscale height of 1 kpc was adopted. This is an important parameter in diffusion theory and isdiscussed in detail in section 2.2.2.For a separation of the Arms (radially) of d , and a standard deviation equal to the scaleheight, σ , the GCR intensity, I , at the centre of one of several parallel equally spaced Arms willbe, (adding the contributions from neighbouring arms): I ( SA ) = G ( σ,
0) + 2 G ( σ, d ) + 2 G ( σ, d ) + ..., (1)where G ( σ, x ) ∝ exp − ( x − ¯ x ) / σ is the Gaussian function of x about its mean ¯ x .Similarly, the GCR intensity at the centre of the IA will be: I ( IA ) = 2 G ( σ, . d ) + 2 G ( σ, . d ) + 2 G ( σ, . d ) + ........ (2)Estimates of the differences in the GCR intensities, I ( IA ) and I ( SA ) , based on equations1 and 2 are given for different values of d and σ in table 1. These are expressed as deficits, δ ,given by, δ = 1 − I ( IA ) I ( SA ) . (3) Table 1
Calculated deficits for different values of scale height, σ (standard deviation of particlediffusion) and d the radial separation of the Spiral Arms. σ (kpc) d (kpc) deficit( δ %)1 2 31 3 362 2 02 3 0.1The rather small calculated deficits occur because the inter-arm separations are of similarmagnitudes to the scale heights, σ (see section 2.2.2). The conclusion from table 1 is that onlyfor SA separated by more than 2.5 kpc would we expect a deficit of more than 20%. A detailedcomparison with the experimental data will be given later.Keeping with our simple model (of constant diffusion coefficient, etc) attention can bedrawn to the calculations of Erlykin and Wolfendale (2003) in which different modes of propa-gation were considered and expected proton spectra were estimated for randomly distributed SNin space and time, the GCR being assumed to come from the subsequent supernova remnants.Spiral Arm features were not considered but the spread of predicted spectra would correspondto different local locations of the SN. At GeV energies the range of predicted intensities was ±
20% for normal diffusion and ±
30% for ’anomalous’ diffusion. The lower extreme valueswill correspond roughly to the Spiral Arm modulation situation so, again, a deficit of about20% is indicated. This value is of the same order as those indicated in table 1.4 .2.2 The Cosmic Ray Scale Height
The scale height, σ , is defined as the distance from the median Galactic Plane at which the GCRintensity falls to a fraction e − / of its mid-Plane magnitude. The value is a convolution of thestandard deviation of the source distribution ( ∼ σ from 1 to 2 kpc but others give larger values (e.g. Moskalenkoet al., 2004 give 4-6 kpc). It can be seen from equations 1 and 2 that the deficits decrease rapidlyas the scale height increases.In view of the standard deviation of the SN distribution being 0.6 kpc (see section 2.1) itwould be impossible for σ to be less than this. Much higher values than 1 kpc are not ruledout, however: explanations for the small ’Galactic gradient’ of the GCR intensity, particularlyin the Outer Galaxy, i.e. for Galactocentric distances greater than that for the Sun at radius 8.5kpc, include the possibility of a big scale height (eg Erlykin and Wolfendale, 2011, and earlierreferences therein). Indeed, Strong et al., (2004) suggest a value as high as 20 kpc. However,this could be due to the existence of a 2-component Halo with the Outer, low density regionhaving the very large scale height. The GCR intensity distribution above and below the Planecould then still be close to that for σ = 1 kpc.Hunter et al (1997) fitted a comprehensive GCR propagation model to the EGRET data onthe measured cosmic ray gamma ray intensities. The fit gave a GCR scale height of 1.8 kpc.A useful further estimate of the scale height at the Galactic radius of the Solar System comesfrom radio astronomy (Erlykin and Wolfendale 2003). Here, Beck (2009) gives σ = 1.7 kpc,assuming that there is equipartition in energy between GCR and magnetic fields and a spatiallyconstant GCR proton to electron ratio.We conclude that, at the Galactic radius of the Solar System, values of σ outside the range1 to 2 kpc are unlikely. High energy gamma rays are mainly produced by the interactions of primary GCR with thegas in the interstellar medium. Most gamma rays of energy above 0.3 GeV are produced byGCR primaries of energies of order several GeV. Specifically, Fathoohi et al.(1995) quote meanproton energies of 2.6, 9.0,40 and 200 GeV to produce gamma rays of mean energy 0.3, 1.0,3.0 and 10.0 GeV, respectively. Thus, gamma rays of energy above 1 GeV come mainly fromprotons of energy above 9 GeV (average ∼
20 GeV), i.e. the energies responsible for much of theionization in the Earth’s atmosphere. Since the inter-stellar medium is transparent to gammarays of this energy their intensity depends on the primary GCR intensity. The gas columndensities are known with reasonable accuracy and the gamma ray intensity along a line of sightafter correction for the gas densities then gives an estimate of the primary GCR intensity.5nspection of maps of the Galaxy, eg as given by Gies and Helsel (2005) and by Vall´ee(2005), shows that certain lines drawn from the Sun at particular longitudes pass largely throughIA regions. The two most suitable longitudes are 60 ◦ and 270 ◦ . At these longitudes there is goodSA, IA contrast. The measured gamma ray intensities in these directions will be compared withthose in directions pointing towards the nearby SA to estimate the deficits. The search for SA, IA differences is not a new one. The COS B satellite (Bignami 1975, Bennettet al., 1976) gave early relevant gamma ray measurements and it is appropriate to mention thework here.We (Rogers et al., 1988) and Bloemen et al.,(1989) presented evidence for the spectral shapeof GCR depending on Galactic latitude and SA, IA intensity differences. Our own work gave adifference of spectral exponent between SA and IA of 0.4 ± ◦ (compared with 0 ◦ in the next section) and here the inverse Compton contributionwill also cause difficulties.b) The later data from EGRET (section 2.3.3) are more accurate. The EGRET data have been analysed by Hunter et al., (1997) who gave useful longitudinaldistributions of gamma ray intensities for a range of gamma ray energies and latitudes. Theseinclude measurements in the Galactic Plane with -2 deg < b < b is the Galacticlatitude. Their distributions of gamma ray intensity as a function of Galactic longitude in thisplane are used here to estimate the deficits.To achieve this we take the difference in gamma ray intensity in the Galactic Plane at alongitude pointing towards a region dominated by an IA from a region pointing to a nearbySA. For the 60 ◦ IA region comparison is made with the region centred on 45 ◦ and the 270 ◦ IAregion is compared with the 285 ◦ direction, the 45 ◦ and 285 ◦ regions each pointing towards theSagittarius-Carina (S-C) Galactic Arm.Table 2 gives the deficits estimated from the EGRET data for the two highest energy bands:0.3 to 1 GeV and > Table 2.
Spiral Inter-Arm Directions from the Sun.Key - Arms; S-C Sagittarius-Carina; L ◦ is the Galactic longitude (90-270 ◦ looking outwardsfrom Galactic Centre); d is the radial separation of the centres of SA; the estimated deficit is δ (see equation 3 for definition). The uncertainties in each case are about 10%. The values givenrefer to method (a) and those in brackets to method (b) (see text). L ◦ Adjacent Arms d (kpc) δ (%) (0.3-1 GeV) δ (%) ( > The most recent gamma ray results come from the FERMI-LAT observatory (Mizuno et al.,2011). These workers have examined the local region of the Outer Galaxy: specifically theLocal Arm and the Perseus Arm regions as well as the IA region between the two. For gammaray energies of greater than 0.3 GeV they found similar intensities from the Perseus arm and theIA region, implying a deficit of around zero. They found 15% less emission from the IA regionthan that in the Local Arm, implying a deficit of 15%. Hence, these values indicate deficits dueto IA, SA differences of less than or order 15%.7 .3.5 Other Galaxies
Observations of the structure of our Galaxy from a position within it (i.e. the Earth) are difficultand, in principle, recourse can be made to other galaxies. Some galaxies, viewed end-on, haveimpressive haloes but the measurements yield information about electrons, and magnetic fieldsand electrons, of course, suffer extra energy losses so that their scale heights will be smallerthan those for protons.Of greater interest is the recent measurements of the Large Magellanic Cloud (LMC) byAbdo et al.(2010) using Fermi-LAT. These workers found what appeared to be a scale heightof 0.2 kpc for cosmic rays responsible for gamma rays in the 0.2-20 GeV energy range. Theprimary cosmic rays are plausibly (authors’ term) the origin of the gamma rays by way ofinteractions with the inter-stellar medium and the radiation fields. This implies both cosmic rayprotons and electrons. Such a small scale height, if applied to our own Galaxy, would imply avery large deficit according to equations 1 and 2 with almost zero GCR intensity when the SolarSystem is outside the SA. We examine this possibility.Firstly, the phenomenon is restricted to the environs of 30 Doradus, the well known, ultra-active star forming region. Now many of the properties of the LMC are very different fromthose in the Galaxy (see Chi and Wolfendale, 1993) and, as these workers showed, the ambientcosmic ray flux is down by a factor 5-10 compared with the local flux. The recent Fermi-LATmeasurements have refined this to a factor ∼ The model adopted (see Table 1) gave predicted values of δ in the range 0 to 36% for σ from 1to 2 kpc and for Arm separations of 2 to 3 kpc. The values are, necessarily approximate, for anumber of reasons as well as the inaccurately known parameters:a. Problems with likely differences in diffusion coefficients in the Arm and Inter-Arm re-gions.b. Stochastic differences due to the actual distribution of relevant SN (and SN remnants) asdistinct from their average values.c. Possible effects of Galactic Winds.Turning to the experimental observations, the derivation of the values of δ is necessarilyimprecise. Foreground contributions are not easy to estimate. Nevertheless, a comparison of’observed’ and ’expected’ is made. 8aking the data in Table 2 at face value and averaging we obtain an observed δ = 23 ± σ = 1 kpc and the mean value of d we predict δ = 25 ±
10 %. Thereis thus reasonable agreement between the model and the data. Note that the model will give amuch lower value of the deficit if the GCR scale height is closer to the value of 1.8 kpc fromthe fit to the EGRET data. This is not incompatible with the data in Table 2 which should belooked on as an upper limit rather than a measurement.We conclude that the deficit in Inter-Arm versus Arm intensities over the Galactic circuit ofthe Solar System is most unlikely to have exceeded 30% at cosmic ray energies of several GeV,the energy producing the majority of the ionization in the Earth’s atmosphere.
We have shown above that the changes in the GCR intensity as the Solar System moves fromthe IA to the SA of our Galaxy are of the order of 20%. These match roughly the changes in theintensity observed during the 20th century due to centennial effects and due to the 11 year solarmodulation. It has been shown that changes at this level cause at most a 0.07 ◦ C change in thepresent day mean global temperature (Erlykin et al., 2009b). Therefore, the changes in globaltemperature due to changes in the GCR intensity as we move from the IA to the SA are likelyto be of the same magnitude. We conclude therefore that such changes cannot produce the largechanges at the Ice Age epochs of the past 10 years as postulated by Shaviv and Veizer (2008). Just as the Solar System passes through successive SA, so it oscillates about the Galactic Plane.The period is about 64 Ma (Gies and Helsel, 2005) and the amplitude is ∼
70 pc (Thaddeus andChanan, 1985). Interestingly, there is a cycle of ’fossil diversity’ with a period of 62 ± The Shaviv model of the difference in GCR rate in the IA and SA regions of the Galaxy giveslarge values for the change in the cosmic ray intensity in passing from the Spiral Arm of theGalaxy to the Inter-Arm region. The calculations presented here, using conventional values forGCR diffusion properties, give such changes at the level of 10 to 20% rather than the factor ∼ yearsremains to be found. Such initiation may possibly have an astronomical cause by way of theeffect of GCR of PeV energies on the electrical conditions of the atmosphere. The periods ofincrease here are of order 20 ka occurring every Ma or so. The 20 ka period arises from the rapiddiffusion of the PeV particles which are deemed responsible. 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