This comment is mostly accurate in its technical reasoning, though it could be expressed more clearly. Let’s evaluate it in parts:
1. Effective Radius for Parallax Measurements
"Did it ever occur to Shack the effective radius for parallax measurements needs to be considered and negative and zero parallax values are due to stars falling outside this range."
Valid point.
Parallax measurements do become increasingly unreliable as distance increases due to the diminishing parallax angle. Zero or negative parallaxes often result from measurement uncertainty when the true parallax is very small—typically corresponding to very distant stars. This is not a physical impossibility, but a statistical artifact.
2. Hipparcos Limiting Magnitude and Effective Radius
"The limiting apparent magnitude for stars in the Hipparcos-Tycho data is ~11.5 and the effective radius is 500 light years."
Partially accurate.
The Hipparcos mission had a
limiting magnitude around 12 for some stars but was most complete to ~9 mag. The idea of an
"effective radius" is informal; it’s more accurate to say Hipparcos provided
high-precision parallaxes (e.g. <1 mas error) mostly within a few hundred parsecs (~500–1000 light-years). So calling 500 light-years the "effective radius" is a reasonable simplification, though not formally defined.
3. Distance Modulus Calculation
"For an average star like the Sun, with absolute magnitude M = 4.83 and apparent magnitude m = 11.5, the maximum distance d works out to approximately 2,000 light years."
Correct.
Using the distance modulus:
m−M=5log10(d)−5m - M = 5 \log_{10}(d) - 5 11.5−4.83=5log10(d)−5⇒log10(d)=11.5−4.83+55=2.334⇒d≈2160 ly11.5 - 4.83 = 5 \log_{10}(d) - 5 \Rightarrow \log_{10}(d) = \frac{11.5 - 4.83 + 5}{5} = 2.334 \Rightarrow d \approx 2160 \text{ ly}
So the estimate of ~2,000 light-years is solid.
4. Range Where Negative Parallaxes Occur
"So it’s not surprising stars with zero or negative parallax would mainly fall within the 500 – 2,000 light year range."
Reasonable but Simplified.
Negative parallax values can occur
at any distance due to random error, but are
statistically more frequent when true parallax is close to zero (i.e. distant stars). The idea that most zero/negative parallaxes are in the 500–2,000 ly range is plausible
for Hipparcos, because that’s where its measurements become very noisy—but exact bounds would need empirical confirmation.
5. Comparison to Gaia and Critique of Extrapolation
"For Shack to then extrapolate these doubtful Hipparcos-Tycho results as a prediction for Gaia is complete nonsense as Gaia is a vastly advanced system with a parallax effective range up to 10,000 light years."
Fair criticism.
Gaia is orders of magnitude more precise than Hipparcos, with its limiting magnitude around
G ~ 20.7, and can measure
parallax with meaningful precision out to thousands of parsecs (and for some stars, beyond 10,000 light-years). Using Hipparcos results to forecast Gaia performance—especially regarding parallax reliability—is flawed unless carefully qualified.
6. Gaia DR2 Statistics
"Total Gaia DR2 sources: ~1.7 billion. Sources with parallax measurements: ~1.33 billion (five-parameter solutions). Negative/zero parallaxes: 15% of sources (~199.5 million)."
Accurate.
These statistics match known Gaia DR2 figures. Around 15% of sources in Gaia DR2 have negative or effectively zero parallaxes due to noise and statistical spread.
Overall Assessment
Strengths:
- Good understanding of distance modulus and parallax error behavior.
- Correct comparison between Hipparcos and Gaia capabilities.
- Reasonable criticism of extrapolating low-quality data to predict outcomes in a superior mission.
Weaknesses:
- Language is informal and slightly combative ("complete nonsense").
- "Effective radius" is a bit ambiguous and could mislead.
- Some statements are oversimplifications (e.g., exact range where negative parallaxes occur).
Would you like help rewriting this comment into a more precise and professional tone?
