Homologous Cluster Expansion Age
Estimate a homologous ballistic expansion age from radius and outward speed; gravity, acceleration, projection and initial size are excluded.
Description
A homologous ballistic expansion estimate treats a cluster's present radius as distance traveled at its outward speed.
A homologous ballistic expansion estimate treats a cluster's present radius as distance traveled at its outward speed. The radius-to-speed timescale is therefore a model age rather than a dated formation measurement.1
Estimate a homologous ballistic expansion age from radius and outward speed; gravity, acceleration, projection and initial size are excluded.
When to use Homologous Cluster Expansion Age
Use this tool to estimate a homologous ballistic expansion age from radius and outward speed; gravity, acceleration, projection and initial size are excluded.
Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
How to use Homologous Cluster Expansion Age and understand its results
- Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
- Enter clusterRadiusParsecs, expansionKmPerSecond using the field table and calculation rules, then run the tool.
- Read expansionAgeMillionYears. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| clusterRadiusParsecs | Cluster radius parsecs | number | Required |
| expansionKmPerSecond | Expansion km per second | number | Required |
Enter positive radius parsecs and outward speed km/s. The tool converts parsecs to km, divides by speed and then by a 365.25-day Julian year and one million. Return million years.
ageMyr=radiusPc × kmPerPc/expansionKmPerSecond/secondsPerJulianYear/10⁶ Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| expansionAgeMillionYears | Expansion age million years | number |
{
"input": {
"clusterRadiusParsecs": 1,
"expansionKmPerSecond": 1
},
"output": {
"expansionAgeMillionYears": 0.9777922216807892
}
}Limitations and assumptions
Gravity, acceleration, initial size and projection are excluded. A present expansion speed need not equal the historical speed, and membership/velocity measurement is not evaluated.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Moving Cluster Distance: Solve a moving-cluster distance from radial velocity and proper motion toward the convergent point; coherent bulk motion and negligible expansion are assumed. For a complementary task, use Rectilinear Astrometric Epoch Propagation: Propagate a Cartesian constant-space-velocity astrometric state using RA* proper motion and Julian years; light-time, gravity and reference-frame precession are excluded.
References
-
Homologous Cluster Expansion Age — tool.io
Similar or alternative tools
- Moving Cluster Distance
Solve a moving-cluster distance from radial velocity and proper motion toward the convergent point; coherent bulk motion and negligible expansion are assumed.
- Rectilinear Astrometric Epoch Propagation
Propagate a Cartesian constant-space-velocity astrometric state using RA* proper motion and Julian years; light-time, gravity and reference-frame precession are excluded.