Homepage of the International Space Science Institute (ISSI) located in Bern, Switzerland
ISSI is a scientifically independent and neutral Space- and Earth Science institute that advances science by facilitating open multi-disciplinary discourse in a stimulating environment, reaching out towards new scientific horizons.
The great auroral display seen in Augsburg on 6 March 1582, reproduced in Usoskin et al. (2023) with permission from Zentralbibliothek Zürich, Department of Prints and Drawings/Photo Archive (shelfmark: ZB Graphische Sammlung (GSB), PAS II 19/4).
Earliest Records of Solar Events
The Sun often produces eruptive events on different energetic and temporal scales. It might, however, also produce events, so-called extreme solar events, whose energy could be orders of magnitude greater than anything we have observed during recent decades. But what is an extreme solar event? How strong can they be and how often do they occur?
To find answers to these and other questions, the ISSI team around Fusa Miyake from Nagoya University in Japan and Ilya Usoskin from Oulu University in Finland went back, far back in time.
Using a combined approach with so far unused measured and archival data, the team studies extreme space weather events that would have catastrophic impact not only on our astronauts and their equipment, but also on our power and communications infrastructure here on the ground.
The examined historical records date back over three millennia! One significant finding is the earliest documented reports of candidate aurorae known today, with a Babylonian astronomer reporting a “red glow” in 567 BCE and possible auroral sightings in Assyrian cuneiform tablets from 679–655 BCE. Additionally, the Bamboo Annals, an ancient Chinese text, describe a celestial event involving a “five-coloured light” in the last year of King Zhāo of the Zhōu Dynasty.
These reports have been correlated with modern records and analysed to determine their likelihood as auroral events, providing insight into ancient space weather occurrences. This research not only extends our space weather chronology but also suggests the existence of a solar minimum around 810–720 BCE, termed the “Neo-Assyrian Grand Minimum“, challenging previous understandings of solar activity during that period.
Read more about this fascinating undertaking in: Usoskin, I., Miyake, F., Baroni, M. et al. Extreme Solar Events: Setting up a Paradigm. Space Sci Rev 219, 73 (2023). https://doi.org/10.1007/s11214-023-01018-1
Normalized 3D electron density distribution resulting from tomographic inversion of polarized-brightness coronagraph images using the six-spacecraft “Solar Ring” configuration. Figure adjusted from ISSI Bern workshop results by Palmerio, Barnes, et al.
A Trailblazing Journey to Decode Coronal Mass Ejections in 3D
In a novel cross-disciplinary effort, the ISSI Team around Erika Palmerio and David Barnes is revolutionizing our understanding of Coronal Mass Ejections (CMEs), powerful solar eruptions with significant space weather impacts on Earth. Focusing on the often-overlooked tomography technique, the team utilizes state-of-the-art magnetohydrodynamic simulations and synthetic white-light data to overcome observational limitations. By placing virtual spacecraft strategically, they generate synthetic images, reconstructing CME structures through discrete tomography.
The findings based on their modelling reveal a complex, irregular front in contrast to traditional assumptions. The team aims to evaluate the impact of 3D reconstructions on space weather predictions, comparing them with conventional forward-modelling techniques. With plans to extend analyses to heliospheric imagery, their work promises groundbreaking insights into CME behavior and improved forecasting methods. Stay tuned for further revelations from this innovative endeavor tackled at ISSI Bern!
The standard cosmological model states that massive galaxies contain a large fraction of dark matter. Dark matter is a transparent substance that does not interact through regular baryonic matter and is only detected through its gravitational pull over the stars and the gas.
Image of the relic galaxy NGC 1277. The small blue galaxy in the lower half of the image is close to NGC 1277 in projection only. (Credit: NASA, ESA and M. Beasley)
NGC 1277 is known as the prototype of a relic galaxy, that is a galaxy that has not accreted other galaxies since it formed. Relic galaxies are extremely rare and are the untouched remains of the giant galaxies that populated the early Universe. Since relic galaxies are very important to understand the conditions in the early stages of the Universe, we observed NGC 1277 using an integral field spectrograph. The information encoded in the spectra allowed us to build kinematic maps from which the mass distribution in the inner 6 kpc (20000 light years) of the galaxy was inferred. We discovered that the mass distribution of mass in NGC 1277 corresponds to that of stars, and we placed an upper limit of 5% to the fraction of dark matter that could exist within the probed radius. Our result is compatible with no dark matter at all in NGC 1277.
Cosmological simulations based on the standard model predict that for galaxies with the mass of NGC 1277 we should have found a dark matter mass fraction of at least 10% and perhaps of up to 70%. The lack of agreement between the observations and the expectation constitutes a mystery. We proposed two possible explanations for the fact that NGC 1277 lacks dark matter. The first one is that dark matter was stripped by interactions between NGC 1277 and the gravitational field of the cluster of galaxies to which it belongs. The second possibility is that dark matter was expelled from the galaxy when it formed through the merger of small proto-galactic bodies. None of these explanations is fully satisfactory, so the riddle of the formation of the galaxy lacking dark matter remains unsolved.
References (Open Access): Comerón, S., I. Trujillo, M. Cappellari et al, The massive relic galaxy NGC 1277 is dark matter deficient. From dynamical models of integral-field stellar kinematics out to five effective radii, Astron. Astrophys., Volume 675, A 143, July 2023, https://doi.org/10.1051/0004-6361/202346291
Among these was ISSI Team #562 “First Light at Cosmic Dawn: Exploiting the James Webb Space Telescope Revolution”, composed of astrophysicists and computer scientists, who are working on one of the core science goals of JWST: finding the first stars and galaxies in the Universe. Discussions on the insights from the initial months of JWST data during their first meeting led Team #562 and their collaborators to submit three proposals that were awarded 153 hours of observing time with three complementary JWST observing modes.
The first survey (GO-4111; PI Wren Suess) titled “Medium bands, Mega Science: Spatially-resolved R~15 spectrophotometry of 50,000 sources at z=0.3-12” is a NIRCam imaging program that leverages the power of medium-band filters combined with cosmological lensing of the Abell2744 cluster/UNCOVER field to efficiently map both stellar continuum and nebular line emission from ionised gas for large, unbiased galaxy samples. By simultaneously probing multiple emission lines the JWST data will measure star formation and dust obscuration and chart the growth of galaxies across >10 Gyrs of cosmic history.
GOODS-S field (NIRCam image) Credit: NASA, ESA, CSA, B. Robertson (UC Santa Cruz), B. Johnson (Center for Astrophysics, Harvard & Smithsonian), S. Tacchella (University of Cambridge, M. Rieke (Univ. of Arizona), D. Eisenstein (Center for Astrophysics, Harvard & Smithsonian), A. Pagan (STScI)
The second program obtains spectroscopy with the NIRSpec instrument (GO-4233; PIs de Graaff & Brammer) over existing, public JWST fields: “A complete census of the rare, extreme and red: A NIRCam-selected extragalactic community survey with JWST/NIRSpec”. The main goal is to obtain detailed, spectroscopic information for newly identified galaxies from JWST images to reveal their nature, and doing this at high completeness.
The final program is a combination of the previous two. GO-3516 (PIs Matthee & Naidu) uses slitless spectroscopy at ~3-4 micron over the same galaxy cluster as the first program in order to search for faint, metal-poor emission line sources. The title of this program summarizes its goals: “All the Little Things: Pop III Signatures & the Ionizing Photon Budget of Dwarf Galaxies in the Epoch of Reionization”.
With more than an 8:1 oversubscription rate for proposals in these categories, the successes of ISSI Team #562 are particularly noteworthy. Speaking on behalf of their team members team leaders Pascal Oesch and Michael Maseda highlighted: “The ISSI team meeting was instrumental in putting these successful proposals together, and we are very thankful to the whole ISSI team for providing us with this opportunity.” ISSI is particularly pleased that the first of these three proposals is led by early-career researcher (ECR) Wren Suess, whose participation to the ISSI Team meeting was enabled by ISSI’s dedicated ECR funding line.
Webb NIRCam composite image of Jupiter from three filters – F360M (red), F212N (yellow-green), and F150W2 (cyan) – and alignment due to the planet’s rotation. Credit: NASA, ESA, CSA, Jupiter ERS Team; image processing by Judy Schmidt.
Freshly approved ISSI Team #23-592 “Jupiter’s non-auroral ionosphere” got off to a flying start of its activities with the award of 22 hours with JWST for project GO-3665 (PIs Stallard & Melin). Studying Jupiter’s equatorial ionosphere in more detail with JWST will further the understanding of energy exchange at the top of the atmosphere, by providing improved constraints for ionospheric models. Atmospheric loss occurs only within this upper region, and so characterising the process on Jupiter provides insight into atmospheric erosion and ultimately thresholds the long term evolution of planets both within and outside our own Solar system.
Determining the vertical structure in the ionosphere away from the bright aurora requires a combination of JWST spectral imaging, utilising the NIRSpec instrument’s integral field spectroscopy mode, and spacecraft occultations of the radio signal from Earth. Via JWST project GO-3665, ISSI Team #23-592 plans to measure the ionospheric structure with JWST simultaneously with the first Juno radio occultations of the Jupiter ionosphere on Sep. 7.
In its first year of science operations, JWST has already demonstrated that it is capable of exceeding expectations and making breakthrough observations in many fields of astrophysics.
Looking ahead to the near future, in March 2024 ISSI will organise a workshop on “The chronology of the 1st billion years”. Outlining her expectations for this workshop, ISSI Executive Director and workshop convenor Antonella Nota, says: “JWST was designed to shed (IR) light on what happened in the early stages of the Universe. Now that most observations from the first JWST cycle have been completed, the time is ripe to convene at ISSI all the cosmology experts with early JWST data, to discuss and distill our current understanding of the formation and early evolution of the first stars and galaxies. At ISSI, we felt that this topic was so important that we are dedicating to it our very first Breakthrough Workshop, a workshop that is aimed at addressing one big question in science” Antonella Nota adds: “ISSI is the perfect place to hold such important conversations, by offering a neutral and welcoming environment, and advancing science – one big question at a time.
The ISSI staff look forward to hosting this workshop and to many further exciting JWST results from the ISSI community.
Thirty International Teams have been selected by the ISSI Science Committee for implementation from the proposals received in response to the 2023 call.
As one of ISSI’s and ISSI-BJ’s tools, International Teams of up to 15 scientists address specific self-defined problems in the Space and Earth Sciences, analyzing data and comparing these with models and theories. The teams work together in an efficient and flexible format with typically 2-3 one-week meetings over two years. The results of the studies are published in the peer-reviewed literature.
The next call for proposals will be issued in January 2024.
The Earth’s magnetosphere shields our planet from hazardous space weather effects caused by solar disturbances and energetic particles. However, the global structure of the magnetosphere is still extremely difficult to describe. Major challenges include the scarcity of data sets, as well as the breadth of physical processes that need to be taken into account. Our ISSI Team explores various approaches that help to mitigate these challenges. Recent publications from our ISSI Team provide new insights into how to extract information about global magnetospheric and ionospheric structures, and how to combine global data analysis and global modeling in meaningful ways. The new results suggest potentially transformative ways to work with global datasets, develop new global models, and improve the accuracy of the current global models.
A paper by Samsonov et al. (2022) uses global X-ray imaging of the Earth’s magnetopause as a novel method that will provide us with knowledge about the shape of the magnetopause. The authors use two numerical global MHD models (SWMF and LFM) to simulate the X-ray emissivity in the magnetosheath and cusps, which are sources of soft X-rays due to charge exchange between solar wind ions and exospheric neutrals. Methods developed to extract the information about magnetopause location from synthetic X-ray images will allow to use the data from the future soft X-ray imagers for monitoring of large areas of the magnetopause. This methodology will allow to validate/modify our current modeling tools and approaches and revolutionize the understanding of magnetospheric response to external driving conditions.
A paper by Holappa and Buzulukova (2022) combines 24 years of observations of energetic particle measurements by NOAA POES satellites with simulation results from a global model of the Earth’s magnetosphere to study the effect of the interplanetary magnetic field (IMF) By component on the ring current. The authors showed that there is an explicit By-dependence of the Dst index, which is a measure of the ring current intensity, and that this dependence can be accounted for by a modified solar wind coupling function that includes a correction factor depending on the dipole tilt and IMF By. This study provides a novel contribution to understanding the complex and seasonally varying effects of IMF By on the magnetospheric dynamics by means of combining global datasets and global models.
A recent study by Stephens et al. (2023) uses machine learning techniques for data-mining of 26 years of magnetometer data from multiple satellites to reconstruct the global structure and evolution of reconnection sites, called X-lines, as well as different types of magnetic nulls, called O-lines, in the magnetotail. The study compares the reconstructed location of X-lines and O-lines with observations from MMS mission and finds a good agreement in most cases. The results from the study have potential to revolutionize our understanding of reconnection process on a global level, suggesting that reconnection in the magnetotail is reproducible with historic data sets, and the global 3D structure of the magnetospheric reconnection is reflected in global activity indices, their trends, and the solar wind energy input.
2D histograms of electron density observed by COSMIC data on the test set versus those predicted by the IRI model (a), and the novel neural network NET model (b). (c) Cumulative distribution of ratios between the IRI model and the COSMIC data on the test set; (d) Cumulative distribution of ratios between the developed NET model and the COSMIC data on the test set. Credit: Smirnov et al., 2023, Nature Scientific Reports (CC BY 4.0)
A recent paper by Smirnov et al. (2023) presents a novel neural network model of electron density in the topside ionosphere. The model has been developed and tested using 19 years of GNSS radio occultation data. The model consists of four parameters that describe the shape, height, and gradient of the F2-peak. The model is tested against in situ measurements from several missions and shows excellent agreement with the observations, outperforming the state-of-the-art International Reference Ionosphere (IRI) model by up to an order of magnitude, especially at 100-200 km above the F2-layer peak. This study provides a paradigm shift in ionospheric research, by demonstrating that ionospheric densities can be reconstructed with very high fidelity with the neural network model. The new model could be valuable for a variety of applications, including space weather forecasting, satellite navigation, and communication systems.
Contact: Natalia Buzulukova
References:
Holappa, L., and N. Y. Buzulukova (2022) “Explicit IMF By-dependence of energetic protons and the ring current.” Geophysical Research Letters, 49 (8), https://doi.org/10.1029/2022GL098031
Samsonov, A., Sembay, S., Read, A., Carter, J. A., Branduardi-Raymont, G., Sibeck, D., & Escoubet, P. (2022). Finding magnetopause standoff distance using a Soft X-ray Imager: 2. Methods to analyze 2-D X-ray images. Journal of Geophysical Research: Space Physics, 127, e2022JA030850. https://doi.org/10.1029/2022JA030850
Smirnov, A., Shprits, Y., Prol, F. et al. A novel neural network model of Earth’s topside ionosphere. Sci Rep13, 1303 (2023). https://doi.org/10.1038/s41598-023-28034-z
Stephens, G. K., Sitnov, M. I., Weigel, R. S., Turner, D. L., Tsyganenko, N. A., Rogers, A. J., et al. (2023). Global structure of magnetotail reconnection revealed by mining space magnetometer data. Journal of Geophysical Research: Space Physics, 128, e2022JA031066. https://doi.org/10.1029/2022JA031066
Earth’s magnetic environment is filled with a symphony of sound that we cannot hear. All around our planet, ultralow-frequency waves compose a cacophonous operetta portraying the dramatic relationship between Earth and the Sun. Now, a new citizen science project called HARP – or Heliophysics Audified: Resonances in Plasmas–has turned those once-unheard waves into audible whistles, crunches, and whooshes. Early tests have already made surprising finds, and citizen scientists can join the journey of sonic space exploration to decipher the cosmic vibrations that help sing the song of the Sun and Earth.
When solar plasma strikes Earth, it causes the magnetic field lines and plasma around Earth to vibrate like the plucked strings of a harp, producing ultralow-frequency waves. In 2007, NASA launched five satellites to fly through Earth’s magnetic “harp” – its magnetosphere – as part of the THEMIS mission. Since then, THEMIS has been gathering a bounty of information about plasma waves across Earth’s magnetosphere.
The frequencies of the waves THEMIS measures are too low for our ears to hear, however. So the HARP team sped them up to convert them to audible sound. By using an interactive tool developed by the team, you can listen to these waves and pick out interesting features you hear in the sounds. Humans are often better at picking out interesting wave patterns by ear than by eye – and can even do better than computers at identifying complex patterns that emerge during extreme solar events.
To start exploring these sounds, visit the HARP website.
Above the neutral atmosphere, space is filled with charged particles, which are tied to the Earth’s magnetic field. The particles come from two sources, the solar wind and the Earth’s upper atmosphere. Most of the solar wind particles are deflected by the Earth´s magnetic field, but some can penetrate into near-Earth space. The ionized layer of the upper atmosphere is continuously ejecting particles into space, which have low energies and are difficult to measure. We investigate the relative importance of the two charged particle sources for the dynamics of plasma processes in near-Earth space. In particular, we consider the effects of these sources in magnetic reconnection.
Magnetic reconnection allows initially separated plasma regions to become magnetically connected and mix, and converts magnetic energy to kinetic energy of charged particles. Magnetic reconnection is the main driver of geomagnetic activity in the near-Earth space, and is responsible for the release of energy that drives a variety of space weather effects. We highlight the fact that plasma from the ionized upper atmosphere contributes a significant part of the density in the key regions where magnetic reconnection is at work, and that this contribution is larger when the geomagnetic activity is high.
Main regions of the Earth’s magnetosphere. Ionospheric ions (light blue) escape and fill the outer magnetosphere until they exit the Earth space environment. Credit: Toledo-Redondo et al. (2021)
Thanks to MMS mission, combined with high-performance numerical modelling, we now understand much better how ionospheric ions modify the reconnection process at a microphysical level. Ionospheric ions circulating in the magnetosphere are accelerated at reconnection sites and constitute a significant sink of energy for the reconnection process. In addition, depending on the ion mass, initial energy, and where the ions are entrained in a reconnection site, different energization mechanisms, some of them more efficient than others, come into play.
We still understand relatively little about how these recent discoveries of the magnetic reconnection microphysics shape the magnetosphere system as a whole. The impact of cold ions is still an open field of research, as cold ions introduce a new length-scale and many plasma processes depend on the coupling between different scales.
There is yet another ionospheric population, which is even less understood: cold electrons. They also outflow from the ionosphere, and these are even harder to characterize than cold ions. Electrons play crucial roles on magnetic reconnection and wave generation in the magnetosphere. So far, because of the immense difficulty of observing these low-energy electrons, the effects of cold electrons remain largely unexplored.
References:
Toledo-Redondo, S., André, M., Aunai, N., Chappell, C. R., Dargent, J., Fuselier, S. A., et al. (2021). Impacts of ionospheric ions on magnetic reconnection and Earth’s magnetosphere dynamics. Reviews of Geophysics, 59, e2020RG000707. https://doi.org/10.1029/2020RG000707
Open Access: Toledo, S., M. André, N. Aunai, C.R. Chappell, J. Dargent, S.A. Fuselier, A. Glocer, D.B. Graham, S. Haaland, M. Hesse, L.M. Kistler, B. Lavraud, W. Li, T. E. Moore, P. Tenfjord, and S.K. Vines (2021), Hidden atmospheric particles sculpt near-Earth space environment, Eos, 102, https://doi.org/10.1029/2021EO163314
Plasma waves forming in the turbulent foreshock upstream of Earth’s bow shock have long been known to transmit into Earth’s magnetosphere. Yet the exact mechanism allowing their propagation through the shock remained unknown. A recent paper published in Nature Physics, led by Lucile Turc and initiated within the ISSI Team #448, proposes a new scenario to explain the wave transmission.
This study makes use of state-of-the-art numerical simulations and spacecraft observations to investigate the processes at play when foreshock waves interact with Earth’s bow shock. Numerical simulations were performed with the Vlasiator model, developed at the University of Helsinki. The model describes foreshock waves in their global context and allows tracking the waves on their earthward journey. To confirm the numerical results, observations from the Magnetospheric Multiscale mission (MMS) were analysed upstream and downstream of Earth’s bow shock.
The results of the study show that the transmitted foreshock waves retain similar properties downstream of the shock as in the foreshock, and in particular their fast-magnetosonic nature – fast-magnetosonic waves are a class of plasma waves with correlated variations in plasma density and magnetic field strength. At first glance, it may seem that the waves traverse the shock unchanged, as predicted in early works. However, the direction of the wavevectors reverses across the shock, which is inconsistent with a direct transmission.
Figure 1: Overview of near-Earth space, as simulated by the Vlasiator model. The colour map shows the magnetic field north-south component, out of the plane of the simulation domain. The cyan lines indicate the bow shock and magnetopause positions. (Image Credit: L. Turc/The Vlasiator Team)
To understand the wave transmission, one needs to take a closer look at the processes happening when foreshock waves impinge on the shock. It was found that the waves modulate the plasma properties just upstream of the shock, and in particular the Mach number, which controls the shock strength. This results in a periodic variation of the compression of the plasma as it crosses the shock, which in turn creates regions of enhanced and decreased pressure in the downstream. This pressure imbalance launches compression and rarefaction waves, at the same period as the foreshock waves, which travel all the way to the magnetosphere.
This work provides the missing link in the transmission of foreshock waves from their source region upstream of the shock into the Earth’s magnetosphere, thus improving our understanding of near-Earth space dynamics. Solving this open question was one of the main goals of the ISSI Team #448, which gathered for this purpose experts of plasma waves in the different regions of near-Earth space.
Figure 2: Time-position maps of the (a) magnetic field strength, (b) magnetic field By component, (c) magnetic field Bz component and (d) magnetosonic Mach number, extracted from the simulation along the Sun-Earth line. The solid cyan, black and white lines indicate the bow shock position. The foreshock waves moving towards the shock appear as stripes of alternating colours on the right-hand side of panels a-c. Their counterparts in the downstream are visible in panels a-b. Panel d shows the modulation of the magnetosonic Mach number by the foreshock waves as they approach the shock. (Image Credit: L. Turc, published in Nat. Phys.)
Shocks, such as the bow shock forming ahead of Earth’s magnetosphere, are found everywhere in space, near other planets, supernovae remnants or active galactic nuclei, and are one of the main sources of high energy particles in our universe. Understanding how plasma waves interact with a bow shock, how they modify it and how they are transmitted to the other side of the shock brings us crucial new insight into collisionless shock waves in general.
Reference
Turc, O.W. Roberts, D. Verscharen, A.P. Dimmock, P. Kajdič, M. Palmroth, Y. Pfau-Kempf, A. Johlander, M. Dubart, E.K.J. Kilpua, J. Soucek, K. Takahashi, N. Takahashi, M. Battarbee, U. Ganse: Transmission of foreshock waves through Earth’s bow shock, Nature Physics, 2022, https://doi.org/10.1038/s41567-022-01837-z
ESA’s Comet Interceptor mission (launch in 2029) will, for the first time, visit a long period or dynamically new comet (LPC/DNC), one the most pristine objects in our Solar System. DNCs have been stored in the outermost part of our planetary system since they formed 4.5 billion years ago. From there, they enter the inner Solar System for the first time to reveal their primitive structure and composition.
Comet Interceptor will pass through a potentially hazardous region of such a comet’s inner and outer coma. It is therefore important to assess the dust impact risk to the spacecraft and their scientific instruments to aid hazard mitigation strategies. Though models describing the dust environment for space missions are not new, the Comet Interceptor mission is unique. It is the first mission for which the mission’s precise target (a specific comet) could remain unknown until after launch. Naturally, this is a particular problem for determining the expected dust coma because of the many parameters with a broad range of possible values.
A Team led by team members Vladimir Zakharov and Raphael Marschall developed a new model to address this problem. By simulating tens of thousands of possible scenarios, they could statistically determine the scenarios the space mission could encounter. Figure 1 below shows the number of particles of a particular mass expected to hit the spacecraft during the encounter. The solid line shows the median and the different shaded areas the scatter in possible outcomes. The unknown properties of the comet of Comet Intercepter result in significant uncertainties that can be as large as four orders of magnitude. Once a comet has been chosen and characterised using ground-based telescopes, the relevant comet properties can be fed into the model to reduce uncertainties.
Figure 1: Total number of dust particles encountered according to the EDCM along the spacecraft trajectory of spacecraft A as function dust mass. The shaded areas show different percentile ranges within which cases fall. Additionally the orange curve shows the predicted median densities for a Halley type comet.
This new model also allowed the team to determine some fundamental properties of the activity of comets. One of the most accessible measurements that can be performed on a comet is to determine the brightness of the dust coma. This brightness is usually given in a quantity known as Afρ. Yet one would like to convert this brightness into a dust production rate at the comet’s surface. This most recent work shows that Afρ by itself is a bad predictor of the dust production rate. Yet, if, in addition, the dust’s size distribution can be measured, then we can derive relatively accurate values of the dust production rate from Afρ and the dust size distribution. This relationship is shown in Figure 2.
Figure 2: Dust production rate as a function of Afρ and the power law exponent, β, of the dust size distribution. The values of Afρ are slightly offset depending on the power law exponent to show the overlap resulting from β. By itself Afρ is a poor predictor of the dust production rate of a comet.
