Description
Return a thin comoving shell volume term.
Survey geometry combines solid angle, radial distance and a stated coordinate or selection basis. A sky fraction, bin midpoint or thin-shell term is a local geometric quantity rather than an integrated survey volume, observed population or selection-corrected estimate.
Return a thin comoving shell volume term.
When to use this tool
Use Comoving Volume Solid Angle One Shell Term when checking the stated survey-area, bin or comoving-volume term.
How to use the tool and how it works
- Enter transverseComovingDistance, radialComovingThickness, solidAngleSteradians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read shellVolume. Use the output convention below.
Return a thin comoving shell volume term. Require nonnegative transverseComovingDistance/thickness and solid angle in [0,4*pi]; shellVolume = distance²*radialComovingThickness*solidAngle.1
Cosmological distance, volume and lookback-time relations require the appropriate expansion-rate and distance conventions; local factors do not replace integration.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| transverseComovingDistance | Transverse Comoving Distance | Required. Finite number; minimum 0. |
| radialComovingThickness | Nonnegative thin-shell radial thickness in the same comoving length unit as transverseComovingDistance. | Required. Finite number; minimum 0. |
| solidAngleSteradians | Solid Angle Steradians | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shellVolume | Shell Volume | Required. Finite number. |
{
"input": {
"transverseComovingDistance": 100,
"radialComovingThickness": 2,
"solidAngleSteradians": 0.5
},
"output": {
"shellVolume": 10000
}
}Limitations and assumptions
- Use matching comoving length units; this local thin-shell expression is not an integrated finite-shell volume.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Integrate the appropriate cosmological volume element and actual survey mask/selection function for complete coverage or number-count analysis.
References
Similar or alternative tools
- Comoving Bin Volume Share
Return comoving-bin share under an exclusion policy.
- Survey Solid Angle Fraction Tool
Calculate survey solid angle fraction from explicit caller-supplied inputs.