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NASA NTRS2012

Development of a Telescope for Medium-Energy Gamma-ray Astronomy

Since the launch of AGILE and FERMI, the scientific progress in high-energy (Eg greater than approximately 200 MeV) gamma-ray science has been, and will continue to be dramatic. Both of these telescopes cover a broad energy range from approximately 20 MeV to greater than 10 GeV. However, neither instrument is optimized for observations below approximately 200 MeV where many astrophysical objects exhibit unique, transitory behavior, such as spectral breaks, bursts, and flares. Hence, while significant progress from current observations is expected, there will nonetheless remain a significant sensitivity gap in the medium-energy (approximately 0.1-200 MeV) regime; the lower end of this range remains largely unexplored whereas the upper end will allow comparison with FERMI data. Tapping into this unexplored regime requires significant improvements in sensitivity. A major emphasis of modern detector development, with the goal of providing significant improvements in sensitivity in the medium-energy regime, focuses on high-resolution electron tracking. The Three-Dimensional Track Imager (3-DTI) technology being developed at GSFC provides high resolution tracking of the electron-positron pair from gamma-ray interactions from 5 to 200 MeV. The 3-DTI consists of a time projection chamber (TPC) and 2-D cross-strip microwell detector (MWD). The low-density and homogeneous design of the 3-DTI, offers unprecedented sensitivity by providing angular resolution near the kinematic limit. Electron tracking also enables measurement of gamma-ray polarization, a new tool to study astrophysical phenomenon. We describe the design, fabrication, and performance of a 30x30x30 cm3 3-DTI detector prototype of a medium-energy gamma-ray telescope.

Sunter, Stan↗
NASA NTRS2012

Titanium-Water Thermosyphon Gamma Radiation Exposure and Results

Titanium-water thermosyphons are being considered for use in heat rejection systems for fission power systems. Their proximity to the nuclear reactor will result in some gamma irradiation. Noncondensable gas formation from radiation-induced breakdown of water over time may render portions of the thermosyphon condenser inoperable. A series of developmental thermosyphons were operated at nominal operating temperature under accelerated gamma irradiation, with exposures on the same order of magnitude as that expected in 8 years of heat rejection system operation. Temperature data were obtained during exposure at three locations on each thermosyphon: evaporator, condenser, and condenser end cap. Some noncondensable gas was evident; however, thermosyphon performance was not affected because the noncondensable gas was compressed into the fill tube region at the top of the thermosyphon, away from the heat rejecting fin. The trend appeared to be an increasing amount of noncondensable gas formation with increasing gamma irradiation dose. Hydrogen is thought to be the most likely candidate for the noncondensable gas and hydrogen is known to diffuse through grain boundaries. Post-exposure evaluation of one thermosyphon in a vacuum chamber and at temperature revealed that the noncondensable gas diffused out of the thermosyphon over a relatively short period of time. Further research shows a number of experimental and theoretical examples of radiolysis occurring through gamma radiation alone in pure water.

Sanzi, James, L.A↗
NASA NTRS2012

Gamma-Ray Observations of the Orion Molecular Clouds with the Fermi Large Area Telescope

We report on the gamma-ray observations of giant molecular clouds Orion A and B with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. The gamma-ray emission in the energy band between approx 100 MeV and approx 100 GeV is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the Galactic cosmic rays (CRs) and interstellar gas. The gamma-ray production cross-section for the nuclear interaction is known to approx 10% precision which makes the LAT a powerful tool to measure the gas mass column density distribution of molecular clouds for a known CR intensity. We present here such distributions for Orion A and B, and correlate them with those of the velocity-integrated CO intensity (W(sub CO)) at a 1 deg 1 deg pixel level. The correlation is found to be linear over a W(sub CO) range of approx 10-fold when divided in three regions, suggesting penetration of nuclear CRs to most of the cloud volumes. The W(sub CO)-to-mass conversion factor, X(sub CO), is found to be approx 2.3 10(exp 20) / sq cm (K km/s)(exp -1) for the high-longitude part of Orion A (l > 212 deg), approx 1.7 times higher than approx 1.3 10(exp 20) found for the rest of Orion A and B. We interpret the apparent high X(sub CO) in the high-longitude region of Orion A in the light of recent works proposing a nonlinear relation between H2 and CO densities in the diffuse molecular gas.W(sub CO) decreases faster than the H2 column density in the region making the gas "darker" to W(sub CO).

Ackermann, M.↗
NASA NTRS2012

Anisotropies in the Diffuse Gamma-Ray Background Measured by the Fermi LAT

The contribution of unresolved sources to the diffuse gamma-ray background could induce anisotropies in this emission on small angular scales. We analyze the angular power spectrum of the diffuse emission measured by the Fermi LAT at Galactic latitudes absolute value of b > 30 deg in four energy bins spanning 1 to 50 GeV. At multipoles l >= 155, corresponding to angular scales approx < 2 deg, angular power above the photon noise level is detected at > 99.99% CL in the 1-2 GeV, 2- 5 GeV, and 5- 10 GeV energy bins, and at > 99% CL at 10-50 GeV. Within each energy bin the measured angular power takes approximately the same value at all multipoles l >= 155, suggesting that it originates from the contribution of one or more unclustered source populations. The amplitude of the angular power normalized to the mean intensity in each energy bin is consistent with a constant value at all energies, C(sub p) / (I)(exp 2) = 9.05 +/- 0.84 x 10(exp -6) sr, while the energy dependence of C(sub p) is consistent with the anisotropy arising from one or more source populations with power-law photon spectra with spectral index Gamma (sub s) = 2.40 +/- 0.07. We discuss the implications of the measured angular power for gamma-ray source populations that may provide a contribution to the diffuse gamma-ray background.

Ferrara, E. C.↗
NASA NTRS2012

Simultaneous Planck, Swift, and Fermi Observations of X-ray and Gamma-ray Selected Blazars

We present simultaneous Planck, Swift, Fermi, and ground-based data for 105 blazars belonging to three samples with flux limits in the soft X-ray, hard X-ray, and gamma-ray bands, with additional 5 GHz flux-density limits to ensure a good probability of a Planck detection. We compare our results to those of a companion paper presenting simultaneous Planck and multi-frequency observations of 104 radio-loud northern active galactic nuclei selected at radio frequencies. While we confirm several previous results, our unique data set allows us to demonstrate that the selection method strongly influences the results, producing biases that cannot be ignored. Almost all the BL Lac objects have been detected by the Fermi Large Area Telescope (LAT), whereas 30% to 40% of the flat-spectrum radio quasars (FSRQs) in the radio, soft X-ray, and hard X-ray selected samples are still below the gamma-ray detection limit even after integrating 27 months of Fermi-LAT data. The radio to sub-millimetre spectral slope of blazars is quite flat, with (alpha) approx 0 up to about 70GHz, above which it steepens to (alpha) approx -0.65. The BL Lacs have significantly flatter spectra than FSRQs at higher frequencies. The distribution of the rest-frame synchrotron peak frequency (nu(sup s)(sub peak)) in the spectral energy distribution (SED) of FSRQs is the same in all the blazar samples with (nu(sup s)(sub peak)) = 10(exp 13.1 +/- 0.1) Hz, while the mean inverse Compton peak frequency, (nu(sup IC)(sub peak)), ranges from 10(exp 21) to 10(exp 22) Hz. The distributions of nu(sup s)(sub peak) and nu(sup IC)(sub peak) of BL Lacs are much broader and are shifted to higher energies than those of FSRQs; their shapes strongly depend on the selection method. The Compton dominance of blazars. defined as the ratio of the inverse Compton to synchrotron peak luminosities, ranges from less than 0.2 to nearly 100, with only FSRQs reaching values larger than about 3. Its distribution is broad and depends strongly on the selection method, with gamma-ray selected blazars peaking at approx 7 or more, and radio-selected blazars at values close to 1, thus implying that the common assumption that the blazar power budget is largely dominated by high-energy emission is a selection effect. A comparison of our multi-frequency data with theoretical predictions shows that simple homogeneous SSC models cannot explain the simultaneous SEDs of most of the gamma-ray detected blazars in all samples. The SED of the blazars that were not detected by Fermi~LAT may instead be consistent with SSC emission. Our data challenge the correlation between bolometric luminosity and nu(sup s)(sub peak) predicted by the blazar sequence.

Giommi, P.↗
NASA NTRS2010

New Neighbours: Modelling the Growing Population of gamma-ray Millisecond Pulsars

The Fermi Large Area Telescope, in collaboration with several groups from the radio community. have had marvelous success at uncovering new gamma-ray millisecond pulsars (MSPs). In fact, MSPs now make up a sizable fraction of the total number of known gamma-ray pulsars. The MSP population is characterized by a variety of pulse profile shapes, peak separations, and radio-to-gamma phase lags, with some members exhibiting nearly phase-aligned radio and gamma-ray light curves (LCs). The MSPs' short spin periods underline the importance of including special relativistic effects in LC calculations, even for emission originating from near the stellar surface. We present results on modelling and classification of MSP LCs using standard pulsar model geometries.

Venter, C.↗
NASA NTRS2012

Titanium-Water Thermosyphon Gamma Radiation Effects and Results

Titanium-water thermosyphons are being considered for use in heat rejection systems for fission power systems. Their proximity to the nuclear reactor will result in some exposure to gamma irradiation. Non-condensable gas formation from radiation may breakdown water over time and render a portion of the thermosyphon condenser inoperable. A series of developmental thermosyphons were operated at nominal operating temperature with accelerated gamma irradiation exposures on the same order of magnitude that is expected in eight years of heat rejection system operation. Temperature data were obtained during exposure at three locations on each thermosyphon; evaporator, condenser, and condenser end cap. Some non-condensable gas was evident, however thermosyphon performance was not affected because the non-condensable gas was compressed into the fill tube region at the top of the thermosyphon, away from the heat rejecting fin. The trend appeared to be an increasing amount of non-condensable gas formation with increasing gamma irradiation dose. Hydrogen is thought to be the most likely candidate for the non-condensable gas and hydrogen is known to diffuse through grain boundaries. Post-exposure evaluation of selected thermosyphons at temperature and in a vacuum chamber revealed that the non-condensable gas likely diffused out of the thermosyphons over a relatively short period of time. Further research shows a number of experimental and theoretical examples of radiolysis occurring through gamma radiation alone in pure water.

Sanzi, James L.↗
NASA NTRS2013

X-ray Follow-ups of XSS J12270-4859: A Low-mass X-ray Binary with Gamma-ray Fermi-LAT Association

Context. XSS J1227.0-4859 is a peculiar, hard X-ray source recently positionally associated to the Fermi-LAT source 1FGL J1227.9- 4852/2FGL J1227.7-4853. Multi-wavelength observations have added information on this source, indicating a low-luminosity lowmass X-ray binary (LMXB), but its nature is still unclear. Aims. To progress in our understanding, we present new X-ray data from a monitoring campaign performed in 2011 with the XMM-Newton, RXTE, and Swift satellites and combine them with new gamma-ray data from the Fermi and AGILE satellites. We complement the study with simultaneous near-UV photometry from XMM-Newton and with previous UV/optical and near-IR data. Methods. We analysed the temporal characteristics in the X-rays, near-UV, and gamma rays and studied the broad-band spectral energy distribution from radio to gamma rays. Results. The X-ray history of XSS J1227 over 7 yr shows a persistent and rather stable low-luminosity (6 × 1033 d2 1 kpcerg s−1) source, with flares and dips being peculiar and permanent characteristics. The associated Fermi-LAT source 2FGL J1227.7-4853 is also stable over an overlapping period of 4.7 yr. Searches for X-ray fast pulsations down to msec give upper limits to pulse fractional amplitudes of 15−25% that do not rule out a fast spinning pulsar. The combined UV/optical/near-IR spectrum reveals a hot component at approximately 13 kK and a cool one at approximately 4.6 kK. The latter would suggest a late-type K2−K5 companion star, a distance range of 1.4−3.6 kpc, and an orbital period of 7-9 h. A near-UV variability (6 h) also suggests a longer orbital period than previously estimated. Conclusions. The analysis shows that the X-ray and UV/optical/near-IR emissions are more compatible with an accretion-powered compact object than with a rotational powered pulsar. The X-ray to UV bolometric luminosity ratio could be consistent with a binary hosting a neutron star, but the uncertainties in the radio data may also allow an LMXB black hole with a compact jet. In this case, it would be the first associated with a high-energy gamma-ray source.

deMartino, D.↗
NASA NTRS2013

Time-resolved Neutron-gamma-ray Data Acquisition for in Situ Subsurface Planetary Geochemistry

The current gamma-ray/neutron instrumentation development effort at NASA Goddard Space Flight Center aims to extend the use of active pulsed neutron interrogation techniques to probe the subsurface elemental composition of planetary bodies in situ. Previous NASA planetary science missions, that used neutron and/or gamma-ray spectroscopy instruments, have relied on neutrons produced from galactic cosmic rays. One of the distinguishing features of this effort is the inclusion of a high intensity 14.1 MeV pulsed neutron generator synchronized with a custom data acquisition system to time each event relative to the pulse. With usually only one opportunity to collect data, it is difficult to set a priori time-gating windows to obtain the best possible results. Acquiring time-tagged, event-by-event data from nuclear induced reactions provides raw data sets containing channel/energy, and event time for each gamma ray or neutron detected. The resulting data set can be plotted as a function of time or energy using optimized analysis windows after the data are acquired. Time windows can now be chosen to produce energy spectra that yield the most statistically significant and accurate elemental composition results that can be derived from the complete data set. The advantages of post-processing gamma-ray time-tagged event-by-event data in experimental tests using our prototype instrument will be demonstrated.

Pulsed neutrongenerator↗
NASA NTRS2013

The Supercritical Pile Gamma-Ray Burst Model: The GRB Afterglow Steep Decline and Plateau Phase

We present a process that accounts for the steep decline and plateau phase of the Swift X-Ray Telescope (XRT) light curves, vexing features of gamma-ray burst (GRB) phenomenology. This process is an integral part of the "supercritical pile" GRB model, proposed a few years ago to account for the conversion of the GRB kinetic energy into radiation with a spectral peak at E(sub pk) is approx. m(sub e)C(exp 2). We compute the evolution of the relativistic blast wave (RBW) Lorentz factor Gamma to show that the radiation-reaction force due to the GRB emission can produce an abrupt, small (approx. 25%) decrease in Gamma at a radius that is smaller (depending on conditions) than the deceleration radius R(sub D). Because of this reduction, the kinematic criticality criterion of the "supercritical pile" is no longer fulfilled. Transfer of the proton energy into electrons ceases and the GRB enters abruptly the afterglow phase at a luminosity smaller by approx. m(sub p)/m(sub e) than that of the prompt emission. If the radius at which this slow-down occurs is significantly smaller than R(sub D), the RBW internal energy continues to drive the RBW expansion at a constant (new) Gamma and its X-ray luminosity remains constant until R(sub D) is reached, at which point it resumes its more conventional decay, thereby completing the "unexpected" XRT light curve phase. If this transition occurs at R is approx. equal to R(sub D), the steep decline is followed by a flux decrease instead of a "plateau," consistent with the conventional afterglow declines. Besides providing an account of these peculiarities, the model suggests that the afterglow phase may in fact begin before the RBW reaches R is approx. equal to R(sub D), thus providing novel insights into GRB phenomenology.

parameters↗
NASA NTRS2012

FERMI Observations of Gamma -Ray Emission From the Moon

We report on the detection of high-energy γ -ray emission from the Moon during the first 24 months of observations by the Fermi Large Area Telescope (LAT). This emission comes from particle cascades produced by cosmicray (CR) nuclei and electrons interacting with the lunar surface. The differential spectrum of the Moon is soft and can be described as a log-parabolic function with an effective cutoff at 2-3 GeV, while the average integral flux measured with the LAT from the beginning of observations in 2008 August to the end of 2010 August is F(greater than100 MeV) = (1.04 plus or minus 0.01 [statistical error] plus or minus 0.1 [systematic error]) × 10(sup −6) cm(sup −2) s(sup −1). This flux is about a factor 2-3 higher than that observed between 1991 and 1994 by the EGRET experiment on board the Compton Gamma Ray Observatory, F(greater than100 MeV)≈5×10(sup −7) cm(sup −2) s(sup −1), when solar activity was relatively high. The higher gamma -ray flux measured by Fermi is consistent with the deep solar minimum conditions during the first 24 months of the mission, which reduced effects of heliospheric modulation, and thus increased the heliospheric flux of Galactic CRs. A detailed comparison of the light curve with McMurdo Neutron Monitor rates suggests a correlation of the trends. The Moon and the Sun are so far the only known bright emitters of gamma-rays with fast celestial motion. Their paths across the sky are projected onto the Galactic center and high Galactic latitudes as well as onto other areas crowded with high-energy gamma-ray sources. Analysis of the lunar and solar emission may thus be important for studies of weak and transient sources near the ecliptic.

fermi↗
NASA NTRS2014

Detailed Investigation of the Gamma-Ray Emission in the Vicinity of SNR W28 with FERMI-LAT

We present a detailed investigation of the Gamma-ray emission in the vicinity of the supernova remnant (SNR) W28 (G6.4−0.1) observed by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope. We detected significant γ -ray emission spatially coincident with TeV sources HESS J1800−240A, B, and C, located outside the radio boundary of the SNR. Their spectra in the 2-100 GeV band are consistent with the extrapolation of the power-law spectra of the TeV sources. We also identified a new source of GeV emission, dubbed Source W, which lies outside the boundary of TeV sources and coincides with radio emission from the western part of W28. All of the GeV Gamma-ray sources overlap with molecular clouds in the velocity range from 0 to 20 km s (exp−1). Under the assumption that the Gamma-ray emission toward HESS J1800−240A, B, and C comes from 3.14(exp0) decay due to the interaction between the molecular clouds and cosmic rays (CRs) escaping from W28, they can be naturally explained by a single model in which the CR diffusion coefficient is smaller than the theoretical expectation in the interstellar space. The total energy of the CRs escaping from W28 is constrained through the same modeling to be larger than is approximately 2 × 10(exp49) erg. The emission from Source W can also be explained with the same CR escape scenario.

cosmic rays↗
NASA NTRS2014

Characterization of the Inner Knot of the Crab: The Site of the Gamma-Ray Flares?

Subsequent to the detections AGILE and Fermi/LAT of the gamma-ray flares from the Crab Nebula in the fall of 2010, this team has been monitoring the X-Ray emission from the Crab on a regular basis. Initially X-Ray observations took place once per month when viewing constraints allowed. More recently observations with Chandra and HST have taken place four times per year. There have been notable exceptions, e.g. in April of 2011 and March 2013 when we initiated a set of Chandra Target of opportunity observations in conjunction with bright gamma-ray flares. Often Keck observations were obtained. The aim of this program to characterize, in depth, the X-ray, optical, and infrared variations that take place in the nebula, and, by so doing, determine the regions which contribute to the harder X-ray variations and, if possible, determine the precise location within the Nebula of the origin of the gamma-ray flares. As part of this project members of the team have applied Singular Value Decomposition techniques to sequences of images in order to more accurately characterize features and their behavior. The current status of the project will be discussed highlighting studies of the inner knot and possible correlations with the gamma-ray flares.

Chandra↗
NASA NTRS2013

High-Energy Gamma-Ray Emission From Solar Flares: Summary of Fermi LAT Detections and Analysis of Two M-Class Flares

We present the detections of 19 solar flares detected in high-energy gamma rays (above 100 MeV) with the Fermi Large Area Telescope (LAT) during its rst four years of operation. Interestingly, all ares are associated with fairly fast Coronal Mass Ejections (CMEs) and are not all powerful X-ray ares. We then describe the detailed temporal, spatial and spectral characteristics of the rst two long-lasting events: the 2011 March 7 are, a moderate (M3.7) impulsive are followed by slowly varying gamma-ray emission over 13 hours, and the 2011 June 7 M2.5 are, which was followed by gamma-ray emission lasting for 2 hours. We compare the Fermi-LAT data with X-ray and proton data measurements from GOES and RHESSI. We argue that a hadronic origin of the gamma rays is more likely than a leptonic origin and nd that the energy spectrum of the proton distribution softens after the 2011 March 7 are, favoring a scenario with continuous acceleration at the are site. This work suggests that proton acceleration in solar ares is more common than previously thought, occurring for even modest X-ray ares, and for longer durations.

fermi↗
NASA NTRS2017

Gamma-Ray Astronomy Across 6 Decades of Energy: Synergy between Fermi, IACTs, and HAWC

Gamma Ray Observatories, Gamma-Ray Astrophysics, GeV TeV Sky Survey, Galaxy, Galactic Plane, Source Distribution, The gamma-ray sky is currently well-monitored with good survey coverage. Many instruments from different waveband/messenger (X rays, gamma rays, neutrinos, gravitational waves) available for simultaneous observations. Both wide-field and pointing instruments in development and coming online in the next decade LIGO

Hui, C. Michelle↗
NASA NTRS2017

Fermi Gamma-Ray Pulsars: Understanding the High-Energy Emission from Dissipative Magnetospheres

Based on the Fermi observational data, we reveal meaningful constraints for the dependence of the macroscopic conductivity (sigma) of dissipative pulsar magnetosphere models on the corresponding spin-down rate, epsilon(sup dot). Our models are refinements of the FIDO (Force-free Inside, Dissipative Outside) models, which have dissipative regions that are restricted on the equatorial current sheet outside of the the light-cylinder. Taking into account the observed cutoff energies of all of the Fermi pulsars and assuming that (a) the corresponding gamma-ray pulsed emission is due to curvature radiation at the radiation-reaction-limit regime, and (b) this emission is produced at the equatorial current sheet near the light cylinder, we show that the Fermi data provide clear indications about the corresponding accelerating electric-field components. A direct comparison between the Fermi cutoff energies and the model ones reveals that if sigma increases with epsilon(sup dot) for high epsilon(sup dot)-values, while it saturates for low ones. This comparison indicates also that the corresponding gap width increases toward low epsilon(sup dot)-values. Assuming the Goldreich-Julian flux for the emitting particles, we calculate the total gamma-ray luminosity (L(sub gamma)). A comparison between the dependence of the Fermi L(sub gamma)-values and the model ones on epsilon(sup dot) indicates an increase of the emitting particle multiplicity with epsilon(sup dot). Our modeling, guided by the Fermi data alone, enhances our understanding of the physical mechanisms behind the high-energy emission in pulsar magnetospheres.

Kalapotharakos, Constantinos↗
NASA NTRS2021

Modeling the Prompt Optical Emission of GRB 180325A: The Evolution of a Spike from the Optical to Gamma Rays

The transition from prompt to afterglow emission is one of the most exciting and least understood phases in gamma-ray bursts (GRBs). Correlations among optical, X-ray, and gamma-ray emission in GRBs have been explored, to attempt to answer whether the earliest optical emission comes from internal and/or external shocks. We present optical photometric observations of GRB 180325A collected with the TAROT and RATIR ground-based telescopes. These observations show two strong optical flashes with separate peaks at ∼50 and ∼120 s, followed by a temporally extended optical emission. We also present X-rays and gamma-ray observations of GRB 180325A, detected by the Burst Alert Telescope and X-ray Telescope, on the Neil Gehrels Swift observatory, which both observed a narrow flash at ∼80 s. We show that the prompt gamma-ray and X-ray early emission shares similar temporal and spectral features consistent with internal dissipation within the relativistic outflow (e.g., by internal shocks or magnetic reconnection), while the early optical flashes are likely generated by the reverse shock that decelerates the ejecta as it sweeps up the external medium.

R. L. Becerra↗
NASA NTRS2023

Retrieval of Normalized Gamma Size Distribution Parameters Using Precipitation Imaging Package (Pip) Snowfall Observations During Ice-Pop 2018

Parameters of the normalized gamma particle size distribution (PSD) have been retrieved from the Precipitation Image Package (PIP) snowfall observations collected during the International Collaborative Experiment - PyeongChang Olympics and Paralympic (ICE-POP 2018). Two of the gamma PSD parameters, the mass weighted particle diameter (Dmass) and the normalized intercept parameter NW, have median values of 1.15-1.31 mm and 2.84-3.04 log(mm-1 m-3), respectively. This range arises from the choice of the relationship between the maximum versus equivalent diameter, Dmx-Deq, and the relationship between the Reynolds and Best numbers, Re-X. Normalization of snow water equivalent rate (SWER) and ice water content (W) by NW reduces the range in NW resulting in well fitted power law relationship, between SWER/NW and Dmass and between W/NW and Dmass. The bulk descriptors of snowfall are calculated from PIP observations and from the gamma PSD with values of the shape parameter (μ) ranging from -2 to 10. NASA’s Global Precipitation Measurement (GPM) mission, which adopted the normalized gamma PSD, assumes μ = 2 and μ = 3 in its two separate algorithms. The mean fractional bias (MFB) of the snowfall parameters changes with μ, where the functional dependence on μ depends on the specific snowfall parameter of interest. The MFB of the total concentration was underestimated by 0.23-0.34 when μ = 2 and by 0.29-0.40 when μ = 3, while the MFB of SWER had a much narrower range (-0.03 to 0.04) for the same μ values.

Snowfall↗