Description
Compare supplied distance moduli and calculate their model-relative distance ratio.
Cosmological quantities depend on scale factor, redshift, distance definition and the dimensionless Hubble parameter h. Proper and comoving distances differ at a specified epoch, and h-scaled units differ from the dimensional Hubble constant. A scalar rescaling or model contribution preserves supplied conventions without fitting a cosmology or inferring an observed distance.
Compare supplied distance moduli and calculate their model-relative distance ratio.
When to use this tool
Use Standard Candle Distance Modulus Residual when you already have observedModulus, modelModulus and need to compare supplied distance moduli and calculate their model-relative distance ratio.
How to use the tool and how it works
- Enter observedModulus, modelModulus. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read modulusResidual, observedToModelDistanceRatio. Use the output convention below.
Return delta=observedModulus-modelModulus and 10^(delta/5).1
A distance-modulus difference corresponds to a base-ten logarithmic distance ratio. The two moduli must use the same definition and calibration.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observedModulus | Observed Modulus | Required. Finite number. |
| modelModulus | Model Modulus | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| modulusResidual | Observed-model distance modulus. | Required. Finite number. |
| observedToModelDistanceRatio | 10^(modulusResidual/5); extreme negative residuals may underflow to zero. | Required. Finite number. |
{
"input": {
"observedModulus": 35,
"modelModulus": 30
},
"output": {
"modulusResidual": 5,
"observedToModelDistanceRatio": 10
}
}Limitations and assumptions
- The same magnitude/standard-candle convention is assumed. No candle calibration, extinction, redshift, distance estimate or cosmology is fitted; extreme ratios can underflow to zero.
- 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
Use the complete cosmological model and its parameter, epoch and unit definitions for a physical inference. Review redshift, distance, lensing and spectrum conventions before combining these local terms; they do not perform line-of-sight integration, parameter estimation or uncertainty analysis.
References
Similar or alternative tools
- Magnitude Hubble Parameter Offset
Calculate a supplied Hubble-parameter magnitude offset relative to a reference.
- Cosmology Distance Physical Comoving Label
Crosswalk supplied same-epoch physical and comoving lengths using a scale factor.