Introduction:
Nathan Myhrvold, a remarkable scholar and collaborator on asteroid research, presents his findings and insights.

Background:
Myhrvold’s academic journey began at a tender age, culminating in a PhD in physics from Princeton University. He pursued postdoctoral research with Stephen Hawking before transitioning to the IT industry. Notably, he served as the founding director of Microsoft Research Lab.

Retirement and Return to Science:
Myhrvold retired from the corporate world at a relatively young age to rededicate himself to scientific pursuits. His diverse interests led him to become a world expert in dinosaurs, as well as the physics and chemistry of cooking. His acclaimed book, Modernist Cuisine, along with its recent companion, Modernist Bread, showcases his expertise in culinary arts.

Asteroid Research Collaboration:
Myhrvold’s collaboration with Zeljko Ivezic and other researchers at the University of Washington focuses on asteroid research. His findings shed light not only on asteroids but also on the scientific process and its potential for improvement.

WISE Mission:
The Wide-field Infrared Survey Explorer (WISE) mission utilized an infrared space telescope for various scientific investigations. Initially aimed at studying the mid-infrared sky, the mission encountered a coolant leak, prompting a shift in objectives.

Data Abundance and Significance:
NEOWISE, initially designed for celestial mapping, has provided valuable asteroid observations, resulting in diameter and albedo measurements for approximately 164,000 asteroids. This data collection is substantial, surpassing all other sources combined and offering a unique resource for asteroid studies.

Mission Phases and Data Variations:
The NEOWISE mission experienced different phases, impacting data acquisition and availability. The full cryogenic phase allowed measurements across four infrared bands, followed by a brief three-band period and a prolonged two-band phase. Data discrepancies exist between the original papers and the Planetary Data System (PDS) archive, including missing asteroids and newly added ones.

Parameter Variations:
Asteroid parameters, such as diameter and albedo, exhibit notable changes between the original publications and the PDS archive. These variations highlight the need for cautious interpretation and cross-referencing of data sources.

Modeling Variations and Assumptions:
NEOWISE asteroid data employs various models and band combinations, resulting in 47 distinct modeling scenarios. NETM (Near-Earth Asteroid Thermal Model) and STM (Standard Thermal Model) are commonly used models, with NETM allowing for diameter and beaming parameter derivation and STM assuming a fixed beaming parameter value. Approximately 44% of the results are fully thermal, utilizing all four infrared bands, while 50.7% rely on a single band, requiring assumptions about albedo. Certain combinations of bands and models are considered peculiar, such as fully thermal modeling with only short-wave bands dominated by reflected solar radiation.

Challenges and Considerations:
The Needham model, typically applied to long-wave thermal observations, is adapted for NEOWISE data with the inclusion of an “I” parameter to estimate albedo in bands affected by reflected sunlight. Assumptions regarding albedo can significantly influence the results, emphasizing the importance of cautious interpretation and considering the limitations of single-band data.

Kirchhoff’s Law and Asteroid Temperatures:
The emissivity and albedo of asteroids in the W1 and W2 bands are not directly related, as they don’t obey Kirchhoff’s law. The beaming parameter is introduced as a fudge factor to compensate for the discrepancy between measured and theoretical temperatures.

The Beaming Parameter:
The beaming parameter is a correction factor that accounts for the incorrect temperature measurements of asteroids. A beaming parameter of 0.75 for Ceres and Vesta indicates that their measured temperatures are too high by a substantial factor.

Beaming Mechanisms:
One explanation for the beaming parameter is the preferential reflection of infrared light in a certain direction, similar to retro reflectors on bicycles. A beaming parameter greater than one suggests a rough surface or craters that trap and re-emit light, making the asteroid appear hotter.

Wavelength Bands and Emissivity:
The W1, W2, W3, and W4 bands are used to measure asteroid properties. An emissivity of 0.9 in the W1 and W2 bands indicates that the asteroid reflects mostly sunlight, with minimal thermal emission. Some asteroids have low emissivity in the W1-2 band, as low as 0.1, based on laboratory spectra of meteorites and silicate minerals.

Data Constraints and Assumptions:
For about 70,000 results, it’s necessary to assume the IR albedo value due to insufficient data to derive it directly. In some cases, assumptions are made about all parameters except the diameter, relying on prior knowledge or limited data.

A Faulty Assumption:
The Neowise project assumed that the infrared albedo of asteroids is a multiple of their visible band albedo. However, this assumption doesn’t hold true for most asteroids.

Scatter in Data:
The relationship between infrared albedo and visible band albedo shows substantial scatter, indicating that the assumption of a linear relationship is inaccurate.

Inconsistent Assumption Values:
The assumed values for the multiplier A varied across different groups of asteroids, indicating that the assumption was not consistently applied.

Better Fit with Offset:
A more accurate assumption would be to consider an offset in addition to a multiplier. This approach resulted in a better fit with the data, according to the corrected Akaike criteria.

Physical Argument:
The physical argument for using a multiple of the visible band albedo was that asteroids are blacker in the infrared. However, the data doesn’t support this argument.

Actual Assumption Values:
The Neowise project didn’t consistently use the assumed values for A. For example, in the case of 134,000 asteroids, the assumed value of A was 1.5, but the actual values used varied.

Data Capping and Band Usage:
The NEOWISE mission data shows two groups of asteroids: those with visible band albedo or IR albedo exactly 1.0 (capped) and those with different values (uncapped). Some papers followed the capping rule, while others did not, resulting in inconsistencies in the data analysis.

Assumptions and Exceptions:
Assumptions regarding the beaming parameter (dv-i) were not consistently followed. Most papers assumed a dv-i value of 1, but there were exceptions, with some papers using a value of 1.2. These exceptions lacked documentation and appeared to be arbitrary.

Band Discarding:
Only 3% of asteroids with all four bands had models using all four bands. The 40% rule led to the discarding of entire bands of data if they had less than 40% of the maximum number of data points. This rule was applied within each epoch, regardless of whether the low data count was due to instrument limitations or other factors.

Epoch Division:
The division of data into epochs was arbitrary and not based on asteroid properties. This led to inconsistencies in band usage across epochs, as different bands might be discarded in different epochs for the same asteroid.

Cosmic Ray Influence:
The reason for discarding bands with low data counts was attributed to cosmic rays, but the mechanism for this influence was unclear. The overall low data count in some bands, even when combining all observations, suggests that the 40% rule may have been overly restrictive.

Conclusion:
The NEOWISE mission data analysis was affected by several biases and inconsistencies. These included data capping, assumptions and exceptions, band discarding, epoch division, and the influence of cosmic rays. These factors may have impacted the accuracy and completeness of the results obtained from the mission.

Model Accuracy Verification:
Accuracy of asteroid thermal modeling is verified by comparing model results to known cases of asteroid size measurements. Known cases include radar occultation, spacecraft measurements, and radar measurements. Data from these known cases is used to assess the accuracy of the thermal modeling.

Discrepancies in Diameter Estimates:
A table presented in a paper shows a significant number of asteroids with diameters ending in 000, coinciding with previously measured Ross diameters. The odds of this occurrence by chance are extremely low, suggesting intentional manipulation.

Evidence of Manipulation:
Other examples of asteroid diameters being altered or replaced with previous measurements are presented. In 2015, Nathan Myhrvold brought these discrepancies to the attention of the relevant authorities. In 2016, a PDS (Planetary Data System) update omitted or modified diameter values, attributing them retroactively to previous papers.

Model Code:
In some cases, a model code of “Dash VB dash” was used for asteroids with diameters matching Ross diameters. This indicates that the diameter was not determined by model fitting but rather set as an assumption. The existence of this model code confirms that the manipulation was intentional.

Implications:
The accuracy of asteroid thermal modeling cannot be reliably determined due to the manipulation of diameter values. This raises concerns about the validity of conclusions drawn from thermal modeling studies. The issue was brought to attention in 2016 by Jean-Luc Margot, a researcher at UCLA.

Observations and Overlap:
WISE satellite observations had 10% overlap to create a sky map. Some asteroids appeared twice within 11 seconds due to the overlap.

Flux Measurement Errors:
Flux measurements showed significant scatter, indicating errors in the data. The estimated errors, provided by the WISE pipeline, also varied widely.

Statistical Analysis:
A z-test was conducted to analyze the standard deviations of the flux measurements. The results showed that many observations had standard deviations significantly higher than expected, up to 46 sigma. A histogram of the z-statistics revealed a non-normal distribution, better fitted by a Student’s t distribution.

Errors in Flux Estimates:
The standard deviations of the flux measurements were much larger than expected. These errors were not specific to asteroids but were also observed for stars.

Reason for Errors:
The WISE sensors were designed for an infrared map of the sky, not specifically for asteroid observations. The errors were likely due to the use of a single exposure instead of multiple co-added frames.

Curve Fitting Issues:
In many cases, the NEOWISE model curve fits poorly with the observed asteroid flux data. A significant number of asteroids had residuals of the same sign in all four bands, indicating a systematic error.

Conclusion:
The WISE satellite flux errors are significant and affect the accuracy of asteroid characterization. The errors are likely due to the design and use of the WISE sensors. Poor curve fitting adds to the uncertainty in asteroid characterization.

Assumptions vs. Data Feedback Loop:
If an assumption is used as a constraint, no amount of data can alter that prior. The data does not contribute to the final result when constrained by assumptions.

Multiple Bands of Data and Fitting Issues:
When multiple bands of data are available, the model may fit three bands but fail to fit the fourth for various reasons. Calculating the mean of a cloud of points is analogous to this situation.

Assessing Consistency in Flux Calculation:
Calculating flux using a consistent method is essential to avoid systematic errors. Histogram analysis of residuals across all bands can reveal any systematic differences in flux calculations.

Constraints and Residuals:
For every constraint that places a result below all data points, there is another constraint placing it above all points. This balance suggests no systematic bias in flux calculations.

Visible Band Albedo Calculations:
The visible band albedo for a spherical asteroid can be calculated using absolute visible magnitude, diameter, and visible band albedo. However, this calculation does not always align with NEOWISE results, indicating potential issues.

Albedo and Diameter Changes:
Plotting albedo changes versus fish allows for analysis of the relationship between albedo and diameter changes. Plotting delta PV over PV results in a cloud of points that can be further analyzed to understand the relationship between albedo and diameter changes.

NEOWISE and Ross Diameter Comparison:
Comparing NEOWISE diameters to Ross diameters revealed a systematic error of about 4% for asteroids with both measurements. Most asteroids lack Ross diameter data, making it challenging to assess the accuracy of NEOWISE diameters for the entire population.

Systematic Errors and Random Errors:
Different models and band combinations showed varied systematic and random errors in diameter estimations. Some models exhibited systematic errors in specific size ranges or deviation levels.

Limitations and Future Work:
The NEOWISE data set has limitations and requires further work to resolve inconsistencies and exceptions. Ongoing efforts aim to address these issues and improve the accuracy of diameter estimations.

Non-Thermal Inertia and Beaming Parameter:
Non-thermal inertia can affect asteroid surface temperatures, influencing diameter estimations. The beaming parameter in thermal models can compensate for various factors, including non-thermal inertia. Unusual beaming parameters may indicate metal-rich asteroids or other unique characteristics.

Challenges in NETA Modeling:
Assuming a spherical shape for asteroids can lead to fitting problems when using minimum chi-square methods. Variations in light curves can be mistaken for errors, causing fitting algorithms to fail. Errors in NEOWISE sigmas can further complicate the fitting process.

Important Considerations:
Variations in light due to rotating asteroids can affect surface area measurements. With enough measurements, these variations average out, and the mean surface area can be obtained. Spherical asteroids have equivalent surface areas to non-spherical asteroids.

Simple Models:
Simple models are useful for screening large numbers of asteroids. Without a shape model, assuming a spherical shape is better than making an incorrect assumption about an ellipsoid shape.

Shape Models:
Shape models require good observations in the visible spectrum. A spherical shape assumption is often more accurate than an incorrect ellipsoid shape assumption.