The particle background of L2

Kevin Burdge August 2020

1 Overview of Langrange points

Consider two orbiting bodies with masses M1 and M2, where M2 < M1. Such a system has five Lagrange points, denoting locations in the potential well where bodies can experience no net force, though only two of these points can form stable minima. L1,L2 and L3 (the three solutions lying directly along the line formed by the two orbiting bodies, all of which are unstable saddle-point solutions) were originally identified by Euler [4], while Lagrange, for which the points are named, identified the final two (potentially stable) solutions at L4 and L5 several years later (note, the stability of these points arises from the Coriolis force corralling objects which attempt to depart the location, which arises the 2ω ˙ r˙ term which arises when computing an acceleration vector in a rotating frame). These notes will not discuss the derivation of the Langrange points (for concise notes on the subject, please see https://map.gsfc.nasa. gov/ContentMedia/lagrange.pdf). The Langrange point of interest in this work, L2 of the Earth- system, is located just outside of the Earth’s orbit around the Sun (see Figure 1), along the line connecting the two bodies at a radius approximated by the expression:

r ≈ apq/3 (1) where r is the distance of the from the lower mass body, a the separation of the two primary bodies, and q the mass ratio of the system q = M2 . This expression only holds in the limit where q << 1, which is the M1 case for the Earth-Sun system, for which r ≈ 1.5 × 1011 cm, about 1 percent of an astronomical unit, or 4 times the Earth-Moon distance. L2 is a particularly attractive location to position space-craft, as it is distant enough from Earth that Earth only occupies a small amount of solid angle in its field of view (≈ 0.19 deg2, which is comparable to the size of the Sun/Moon as seen from Earth). This provides an enormous advantage to astronomical mis- sions positioned at this location for two reasons: 1. the restriction on viewing angle due to the Earth obstructing a large portion of the sky, and 2. the space- craft need not cope with significant change in rate of heating over the course of an orbit as it passes in and out of the Earth’s shadow. One notable disadvantage of the point when compared with missions positioned closer to Earth, is that

1 Figure 1: A basic illustration of the location of the L2 Langrange point in the Earth-Sun system. a denotes the orbital seperation of the Earth and Sun, and r the distance of the Langrange point from the Earth.

because it is further away from Earth, transmitting information back to Earth requires more careful thought than for missions positioned in for example, low Earth orbit. Many of the highest profile space-based astronomical missions were designed to operate at L2, including , Spektr-RG, The James Webb Space Telescope, etc. At a cursory glance, L4 and L5 might also seem like attractive locations to position missions (as they are stable Langrange points); however, their stability comes with the downside that these locations are occupied by a group of asteroids known as Trojans, making them very unattractive locations to park an expensive and delicate space telescope.

2 The particle background of L2 Astronomical sites, be they on the ground or in space, are all accompanied by forms of background. Many ground based observatories which make exquisite observing sites to due to exceptionally good seeing, weather conditions, etc have been rendered relatively useless due to increases in background counts (a good example is Mt. Wilson: see [5]). Most of astronomy (with the exception of neutrino and gravitational wave detectors) has been built around extracting information from photons across a large dynamic range of wavelengths. Some- thing important for any careful astronomer to understand, regardless of the energy regime they work in, are the characteristics and physical origin of the background counts their detector will register, as these counts are important in

2 determining the sensitivity of instruments. Space is accompanied with a background which has location dependent char- acteristics. The remainder of this note will discuss the high energy particle background at L2. High energy ionizing radiation originating from space is gen- erally referred to as a “cosmic ray”, and most of this radiation consists of just a single protons, though some heavier nuclei make up approximately 10 percent of this radiation [2]. The distribution of this background can be seen in Figure 2.

Figure 2: The galactic comsic ray background, as measured by many different experiments. Note that this background is dominated by protons. Taken from [6]

At L2, the two dominant sources of this radiation are the galactic comsmic ray background (hypothesized to originate primarily from supernova remnants, see [2] for further details), and the Sun, which provides a relatively constant source of radiation via the wind as well as more sporadic high energy solar particles (SEPs) which we will discuss in more detail here. SEPs are thought to originate from two primary mechanisms: particles which originate in short flares at the Sun’s surface, which are guided by the strongest

3 magnetic field lines emanating from the Sun, and particles which originating from events (CMEs), in which a large quantity of is ejected from the Sun, and forms a shock which disperses radiation as it propa- gates away from the Sun through previously ejected matter (see Figure 3). The later phenomenon produces elevated counts for several days at a time, whereas the more concentrated bursts typically only elevated counts for a few hours. For an excellent review of the subject of solar outbursts, see [3]. Note that these events also produce bremsstrahlung, and thus contribute to the X-ray count background as well. In general, the corona of a G type star like our Sun pro- duces X-rays Krucker2008, and this effect becomes even more pronounced in the geocoronal activity of later type stars, which can often be seen as detectable X-ray sources at distances of several hundred parsecs. It is worth noting that the solar cycle impacts both the measured flux of solar radiation at L2, but also the galactic background. Near solar maximum, the cosmic ray flux actually decreases as a result of the extension of the Sun’s heliosphere [1], but is accompanied by an increase in solar flaring activity.

Figure 3: A schematic of a shock front forming around a coronal mass ejection propagating away from the sun (central figure). On the left, right, and below, are relative particle spectra observed during events, as viewed from different solar longitudes, illustrating the strong position dependence of such an effect. Note that the particle content is dominated by the 1 to 4 MeV range, and the worst case scenario is clearly illustrated by the bottom panel, which represents a face on viewing angle of the CME. This Figure was taken from [3]

An important form of radiation for eROSITA is the X-ray background. Ex-

4 tensive work characterizing this background is described in [7]. In summary, the work performed by [7] found that the softest end of the X-ray background con- sists primarily of a thermal component resulting from diffuse Galactic emission (which is was well modelled with two blackbodies, at 0.07 KeV and 0.2 KeV, respectively). Higher energy emission is dominated by the cosmic background, and is well modelled by a power law with Γ = 1.42. For more precise coefficients for these fits, please see Figure 4, taken from [7]. As discussed above, the Sun also contributes to this background, with a maximum of activity near the solar maximum.

Figure 4: The x-ray background as measured by XMM-Newton, described in the work [7] (from which this Figure was taken). The background is dominated by galactic diffuse emission at low energies (best described by two blackbodies), and transitions to a power-law spectrum originating from the extragalactic x-ray background at higher energies.

In conclusion, the particle background at L2 is comprised of a combination of the cosmic ray background (which is a combination of charged particles con- sisting primarily of protons, and x-ray photons, as seen in figures 4 and 2), and that arising from the Sun, which consists of a relatively constant stream of charged particles originating from the , as well as more stochastic events such as flares and coronal mass ejections which eject high energy so- lar particles. The most important modulation of the background arises from the solar cycle, which both impacts the cosmic ray background by deflecting particles more efficiently when the heliosphere reaches maximum extent, but also resulting in a higher frequency of flaring events at solar maximum. For

5 simulated background count rates as estimated for this environment, please see http://www.mpe.mpg.de/1341347/eROSITA_background_v12.pdf.

References

[1] OPM Aslam et al. Solar modulation of cosmic rays during the declining and minimum phases of solar cycle 23: comparison with past three solar cycles. Solar Physics, 279(1):269–288, 2012. [2] Pasquale Blasi. The origin of galactic cosmic rays. , 21:70, November 2013.

[3] Mihir Desai and Joe Giacalone. Large gradual solar energetic particle events. Living Reviews in Solar Physics, 13(1):3, 2016. [4] Leonhard Euler. De motu rectilineo trium corporum se mutuo attrahen- tium. Novi commentarii academiae scientiarum Petropolitanae, pages 144– 151, 1767.

[5] R. H. Garstang. Mount Wilson Observatory: the sad story of light pollution. The Observatory, 124:14–21, February 2004. [6] A. M. Hillas. Cosmic Rays: Recent Progress and some Current Questions. arXiv e-prints, pages astro–ph/0607109, July 2006.

[7] D. H. Lumb, R. S. Warwick, M. Page, and A. De Luca. X-ray background measurements with XMM-Newton EPIC. , 389:93–105, July 2002.

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