Stellar Magnitude Ontology
Astronomical Measurements
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
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# Stellar Magnitude Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/astronomical-measurements/stellar-magnitude-ontology.html
FLOW StellarMagnitudeOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Stellar Magnitude Ontology
PURPOSE:
Represent stellar magnitude as a logarithmic astronomical brightness quantity, including apparent magnitude, absolute magnitude, flux ratios, photometric zero points, bandpasses, colour indices, bolometric magnitude, distance modulus, extinction, reddening, K-corrections, instrumental magnitudes, detector calibration, variability, uncertainty, provenance, and strict distinctions between magnitude, flux, luminosity, surface brightness and seismic magnitude.
ENTITY StellarMagnitude {
TYPE: DimensionlessLogarithmicPhotometricQuantity
SYMBOL: m_or_M_context_dependent
DIMENSION: dimensionless
DEFINITION:
stellar_magnitude :=
logarithmic_measure_of_stellar_brightness
defined_relative_to_a_photometric_zero_point_or_reference
PROPERTIES:
is_logarithmic
lower_value_generally_means_brighter_source
depends_on_photometric_system
depends_on_bandpass
may_be_apparent_or_absolute
may_have_uncertainty
}
ENTITY ApparentMagnitude {
TYPE: StellarMagnitude
SYMBOL: m
DEFINITION:
magnitude_corresponding_to_observed_flux
in_declared_photometric_band_and_system
}
ENTITY AbsoluteMagnitude {
TYPE: IntrinsicBrightnessMagnitude
SYMBOL: M
DEFINITION:
apparent_magnitude_object_would_have
at_standard_reference_distance
under_declared_extinction_and_bandpass_convention
STANDARD_STELLAR_REFERENCE_DISTANCE:
10 parsec
}
ENTITY BolometricMagnitude {
TYPE: MagnitudeAcrossAllWavelengths
SYMBOL:
m_bol_or_M_bol
RULE:
bolometric_magnitude != single_band_magnitude
}
MAGNITUDE_SCALE_MODEL {
Pogson_relation:
m_1-m_2 =
-2.5*log10(F_1/F_2)
inverse_flux_ratio:
F_1/F_2 =
10^(-0.4*(m_1-m_2))
RULE:
magnitude_scale_is_inverse_logarithmic_brightness_scale
}
FLUX_ZERO_POINT_MODEL {
generic:
m =
-2.5*log10(F/F_0)
inverse:
F =
F_0*10^(-0.4*m)
REQUIRE:
flux_definition
zero_point
photometric_system
bandpass
RULE:
magnitude_without_zero_point_system_and_band MAY be_semantically_incomplete
}
APPARENT_MAGNITUDE_MODEL {
observed:
m_band
dependencies:
source_flux
distance
extinction
bandpass
photometric_system
RULE:
apparent_magnitude_is_observer_dependent_brightness_quantity
}
ABSOLUTE_MAGNITUDE_MODEL {
no_extinction:
m-M =
5*log10(d_pc)-5
rearranged:
M =
m - 5*log10(d_pc) + 5
REQUIRE:
d_pc > 0
RULE:
absolute_magnitude_is_distance_normalised_brightness_quantity
}
DISTANCE_MODULUS_MODEL {
apparent_distance_modulus:
mu =
m-M
no_extinction:
mu =
5*log10(d_pc)-5
extinction_adjusted:
m-M =
5*log10(d_pc)-5+A_band
true_distance_modulus:
mu_0 =
m-M-A_band
inverse:
d_pc =
10^((mu_0+5)/5)
RULE:
apparent_and_true_distance_modulus MUST be distinguished_when_extinction_is_nonzero
}
PHOTOMETRIC_SYSTEM_MODEL {
possible_systems:
AB
Vega
ST
instrumental
survey_specific
REQUIRE:
system_identifier
zero_point_definition
filter_or_band
RULE:
same_numeric_magnitude_in_different_systems MAY correspond_to_different_fluxes
}
AB_MAGNITUDE_MODEL {
definition:
based_on_spectral_flux_density_per_frequency
generic:
m_AB =
-2.5*log10(F_nu/F_nu0)
reference:
F_nu0 defined_by_AB_system
RULE:
AB_magnitude_requires_F_nu_semantics
}
VEGA_MAGNITUDE_MODEL {
reference:
Vega_or_system_specific_Vega_calibration
generic:
m_Vega =
-2.5*log10(F/F_Vega_reference)
RULE:
Vega_zero_point_depends_on_bandpass_and_calibration_realisation
}
ST_MAGNITUDE_MODEL {
definition:
based_on_spectral_flux_density_per_wavelength
RULE:
ST_and_AB_magnitudes_use_different_spectral_flux_density_basis
}
BANDPASS_MODEL {
possible_bands:
ultraviolet
U
B
V
R
I
optical_survey_bands
J
H
K
infrared
custom_filter
response:
filter
detector
optics
atmosphere_when_ground_based
RULE:
magnitude MUST preserve_bandpass
}
SYNTHETIC_PHOTOMETRY_MODEL {
source_spectrum:
F_lambda_or_F_nu
system_response:
S(lambda)
synthetic_flux:
weighted_integral_over_bandpass
magnitude:
derived_from_integrated_flux_and_zero_point
RULE:
photon_counting_and_energy_integrating_conventions MUST be preserved
}
COLOR_INDEX_MODEL {
generic:
colour =
m_band1-m_band2
examples:
B_minus_V
V_minus_K
RULE:
colour_index_is_magnitude_difference
and_not_single_band_magnitude
}
FLUX_RATIO_MODEL {
if_delta_m_known:
F_1/F_2 =
10^(-0.4*delta_m)
examples:
delta_m = 5
implies_flux_ratio = 0.01
for_object_1_minus_object_2_convention
RULE:
sign_order_of_magnitude_difference MUST be preserved
}
LUMINOSITY_MODEL {
flux:
F =
L/(4*pi*d^2)
under_isotropic_Euclidean_context
magnitude_difference_for_equal_distance:
delta_m =
-2.5*log10(L_1/L_2)
when_band_luminosities_and_other_conditions_compatible
RULE:
magnitude != luminosity
}
BOLOMETRIC_MODEL {
bolometric_luminosity:
integrated_over_all_wavelengths
bolometric_magnitude:
M_bol
bolometric_correction:
BC_band =
M_bol-M_band
inverse:
M_bol =
M_band+BC_band
RULE:
bolometric_correction_depends_on_stellar_spectrum_and_band
}
SOLAR_REFERENCE_MODEL {
relative_luminosity:
M_bol-M_bol_sun =
-2.5*log10(L/L_sun)
inverse:
L/L_sun =
10^(-0.4*(M_bol-M_bol_sun))
RULE:
adopted_solar_bolometric_magnitude_reference MUST be preserved
}
EXTINCTION_MODEL {
observed:
m_obs =
m_intrinsic_apparent + A_lambda
corrected:
m_0 =
m_obs-A_lambda
RULE:
extinction_makes_source_appear_fainter_and_increases_magnitude
}
REDDENING_MODEL {
colour_excess:
E(B-V) =
(B-V)_observed-(B-V)_intrinsic
extinction_relation_example:
A_V =
R_V*E(B-V)
RULE:
extinction_law_and_R_V_or_equivalent_parameters MUST be preserved
}
ATMOSPHERIC_EXTINCTION_MODEL {
ground_based:
m_observed =
m_above_atmosphere + k*X
under_simple_linear_extinction_model
WHERE:
k = extinction_coefficient
X = airmass
RULE:
atmospheric_extinction_correction_requires_airmass_and_band_specific_coefficient
}
K_CORRECTION_MODEL {
purpose:
relate_observed_band_magnitude_to_rest_frame_quantity_for_redshifted_source
dependencies:
redshift
source_spectrum
observed_band
rest_band
photometric_system
RULE:
K_correction_is_not_interstellar_extinction
}
INSTRUMENTAL_MAGNITUDE_MODEL {
raw_or_reduced_count_rate:
C
generic:
m_inst =
-2.5*log10(C)
plus_declared_constant_or_exposure_normalisation
RULE:
instrumental_magnitude != calibrated_standard_magnitude
}
PHOTOMETRIC_CALIBRATION_MODEL {
generic:
m_standard =
m_instrumental
+ zero_point
+ colour_term
+ extinction_term
+ other_declared_corrections
REQUIRE:
standard_stars
zero_point
colour_transformation
atmospheric_extinction_when_relevant
RULE:
calibration_equation_and_sign_conventions MUST be preserved
}
DETECTOR_MODEL {
raw:
digital_counts
electrons
processing:
bias_subtraction
dark_subtraction
flat_fielding
cosmic_ray_rejection
aperture_or_PSF_photometry
background_subtraction
output:
calibrated_flux_or_magnitude
RULE:
raw_detector_counts != stellar_magnitude
}
APERTURE_PHOTOMETRY_MODEL {
source_counts:
counts_within_aperture
background:
estimated_from_declared_region
net_counts:
C_net =
C_aperture-C_background_scaled
RULE:
aperture_radius_background_method_and_correction MUST be preserved
}
PSF_PHOTOMETRY_MODEL {
method:
fit_point_spread_function_to_source
suitable_context:
crowded_fields
faint_sources
RULE:
PSF_model_and_fit_quality SHOULD be preserved
}
SATURATION_MODEL {
detector_saturation:
nonlinear_or_clipped_response_for_bright_source
RULE:
saturated_measurement SHOULD be_flagged_and_not_used_as_normal_calibrated_photometry_without_recovery_model
}
VARIABILITY_MODEL {
time_series:
m = m(t)
quantities:
mean_magnitude
amplitude
period
maximum_brightness
minimum_brightness
RULE:
mean_magnitude_method MUST be declared
because_mean_in_magnitude_space_differs_from_magnitude_of_mean_flux
}
MEAN_MAGNITUDE_MODEL {
arithmetic_magnitude_mean:
mean(m_i)
intensity_mean:
convert_magnitudes_to_flux
average_flux
convert_back_to_magnitude
RULE:
arithmetic_mean_magnitude != intensity_mean_magnitude_in_general
}
BINARY_BLEND_MODEL {
combined_flux:
F_total =
F_1+F_2
combined_magnitude:
m_total =
-2.5*log10(
10^(-0.4*m_1)
+ 10^(-0.4*m_2)
)
under_common_zero_point
RULE:
magnitudes MUST_NOT be_added_linearly
}
SURFACE_BRIGHTNESS_DISTINCTION_MODEL {
surface_brightness:
magnitude_per_angular_area
or_flux_per_solid_angle
stellar_magnitude:
integrated_point_source_or_total_source_brightness
RULE:
integrated_magnitude != surface_brightness
}
SPECTRAL_TYPE_CONTEXT_MODEL {
stellar_spectrum:
influences_colour
bolometric_correction
photometric transformations
RULE:
stellar_magnitude_interpretation MAY depend_on_spectral_energy_distribution
}
TEMPORAL_MODEL {
observation_time:
timestamp
variable_star:
magnitude_changes_with_phase
REQUIRE:
time_standard_when_precision_required
RULE:
magnitude_measurement_of_variable_source MUST preserve_observation_time
}
RELATIONSHIPS {
StellarMagnitude -> LOGARITHMICALLY_RELATES_TO -> Flux
ApparentMagnitude -> DESCRIBES -> ObservedBrightness
AbsoluteMagnitude -> NORMALISES -> BrightnessToReferenceDistance
DistanceModulus -> RELATES -> ApparentAbsoluteMagnitudeAndDistance
PhotometricSystem -> DEFINES -> MagnitudeZeroPoint
Bandpass -> QUALIFIES -> Magnitude
ColorIndex -> DIFFERENCE_OF -> TwoBandMagnitudes
Extinction -> INCREASES -> ObservedMagnitude
BolometricCorrection -> MAPS -> BandMagnitudeToBolometricMagnitude
DetectorCalibration -> MAPS -> RawCountsToCalibratedMagnitude
}
SEMANTIC_EQUIVALENCE {
"stellar magnitude" ~= astronomical_photometric_magnitude WHEN stellar_context
"apparent magnitude" ~= observed_brightness_magnitude
"absolute magnitude" ~= reference_distance_magnitude
stellar_magnitude != seismic_magnitude
apparent_magnitude != absolute_magnitude
magnitude != flux
magnitude != luminosity
magnitude != surface_brightness
instrumental_magnitude != calibrated_magnitude
colour_index != magnitude
bolometric_magnitude != single_band_magnitude
}
CONSTRAINTS {
stellar_magnitude_is_dimensionless = true
photometric_system_must_be_defined = true
bandpass_must_be_defined = true
apparent_and_absolute_magnitude_are_not_semantically_equivalent = true
magnitude_and_flux_are_not_semantically_equivalent = true
magnitudes_must_not_be_linearly_added = true
distance_modulus_requires_distance_and_extinction_context = true
instrumental_magnitude_requires_calibration_for_standard_use = true
variable_source_measurement_should_preserve_time = true
uncertainty_should_include_photon_background_calibration_and_model_components = true
}
MEASUREMENT_MODEL {
OBSERVABLE_OR_INFERRED:
ApparentMagnitude
AbsoluteMagnitude
BolometricMagnitude
ColorIndex
DistanceModulus
COMMON_METHODS:
aperture_photometry
PSF_photometry
synthetic_photometry
calibrated_catalogue_photometry
time_series_photometry
RECORD:
celestial_object
object_identifier
magnitude_value
magnitude_type
photometric_system
bandpass
zero_point
observation_time
time_scale
telescope
instrument
detector
exposure_time
raw_counts
background
aperture_or_PSF_method
atmospheric_extinction
interstellar_extinction
reddening
K_correction_when_relevant
calibration_model
quality_flag
uncertainty
provenance
UNCERTAINTY:
measured_or_inferred_stellar_magnitude =
best_estimate +/- uncertainty
}
UNCERTAINTY_MODEL {
sources:
photon_noise
detector_read_noise
background
flat_field
aperture_correction
PSF_model
zero_point
colour_term
atmospheric_extinction
interstellar_extinction
distance
bolometric_correction
source_variability
blending
PROPAGATION:
stellar_magnitude_uncertainty
<- detector_photometric_calibration_extinction_distance_and_model_uncertainties
}
REASONING_RULES {
IF fluxes_F1_F2_positive
THEN magnitude_difference =
-2.5*log10(F1/F2)
IF magnitude_difference_known
THEN flux_ratio =
10^(-0.4*magnitude_difference)
IF magnitude_and_zero_point_flux_known
THEN flux =
zero_point_flux*10^(-0.4*magnitude)
IF apparent_magnitude_distance_pc_known
AND distance_pc > 0
AND extinction_known
THEN absolute_magnitude =
apparent_magnitude
- 5*log10(distance_pc)
+ 5
- extinction
IF absolute_magnitude_apparent_magnitude_and_extinction_known
THEN true_distance_modulus =
apparent_magnitude-absolute_magnitude-extinction
IF true_distance_modulus_known
THEN distance_pc =
10^((true_distance_modulus+5)/5)
IF band_magnitude_and_bolometric_correction_known
THEN bolometric_magnitude =
band_magnitude+bolometric_correction
IF two_compatible_magnitudes_known
THEN combined_flux =
flux(m_1)+flux(m_2)
AND combined_magnitude =
magnitude(combined_flux)
IF raw_counts_and_valid_photometric_calibration_known
THEN calibrated_magnitude =
apply_photometric_calibration(raw_counts)
IF variable_star_time_series_known
THEN compute_declared_mean_amplitude_and_period
preserving_time_and_mean_definition
}
VALIDATION {
CHECK stellar_object_identity
CHECK magnitude_type
CHECK dimensionless_semantics
CHECK photometric_system
CHECK bandpass
CHECK zero_point
CHECK apparent_vs_absolute_magnitude
CHECK magnitude_vs_flux
CHECK magnitude_vs_luminosity
CHECK magnitude_vs_seismic_magnitude
CHECK distance_modulus
CHECK extinction_and_reddening
CHECK bolometric_correction
CHECK instrumental_vs_calibrated_magnitude
CHECK detector_saturation
CHECK blending
CHECK observation_time_for_variable_source
CHECK quality_flag
CHECK uncertainty_representation
}
CONFIDENCE {
definition_confidence: 1.00
logarithmic_relationship_confidence: 1.00
flux_ratio_confidence: 1.00
distance_modulus_confidence: 1.00
photometric_calibration_confidence: 0.99
extinction_correction_confidence: 0.97
bolometric_correction_confidence: 0.97
measurement_context_confidence: 0.98
RULE:
confidence decreases when magnitude type, system, bandpass,
zero point, extinction, distance, calibration,
source variability or uncertainty is missing or ambiguous
}
UPDATE_MODEL {
ON new_measurement:
identify_stellar_object
identify_apparent_absolute_bolometric_or_other_magnitude
attach_photometric_system_and_bandpass
attach_observation_time
preserve_raw_counts_or_flux
identify_detector_and_photometry_method
apply_valid_photometric_calibration
attach_extinction_reddening_and_K_correction_when_relevant
attach_quality_flag
attach_uncertainty
update_stellar_magnitude_state
ON calibration_revision:
preserve_raw_detector_measurements
preserve_previous_zero_point
apply_new_zero_point_colour_and_extinction_terms
recompute_calibrated_magnitudes
update_uncertainty
update_confidence
ON distance_revision:
preserve_apparent_magnitude
update_distance_and_extinction
recompute_absolute_magnitude_and_distance_modulus
update_uncertainty
ON variability_update:
append_time_resolved_magnitude
preserve_time_scale
recompute_declared_mean_amplitude_and_period
preserve_mean_definition
ON bolometric_correction_revision:
preserve_band_magnitude
update_bolometric_correction
recompute_bolometric_magnitude
update_uncertainty
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_domain: StellarMagnitude
canonical_apparent_symbol: m
canonical_absolute_symbol: M
canonical_dimension: dimensionless
interpretation_order:
identify_stellar_object
identify_magnitude_value
identify_apparent_absolute_bolometric_instrumental_or_colour_quantity
identify_photometric_system
identify_bandpass
identify_zero_point
identify_observation_time
identify_raw_or_calibrated_status
identify_extinction_and_reddening
identify_distance_when_absolute_magnitude_or_distance_modulus_involved
identify_bolometric_or_K_correction
identify_variability_and_blending_context
identify_quality_flag
identify_uncertainty
validate_logarithmic_semantics
infer_flux_distance_and_luminosity_relationships
ambiguity_controls:
distinguish_stellar_magnitude_from_seismic_magnitude
distinguish_apparent_from_absolute_magnitude
distinguish_magnitude_from_flux
distinguish_magnitude_from_luminosity
distinguish_integrated_magnitude_from_surface_brightness
distinguish_instrumental_from_calibrated_magnitude
distinguish_colour_index_from_single_band_magnitude
distinguish_bolometric_from_band_limited_magnitude
preserve_object_system_band_zero_point_time_extinction_distance_calibration_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_and_astronomical_stellar_magnitude_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Stellar Magnitude Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_domain
ontology_path
magnitude_scale_model
flux_zero_point_model
apparent_magnitude_model
absolute_magnitude_model
distance_modulus_model
photometric_system_model
AB_magnitude_model
Vega_magnitude_model
ST_magnitude_model
bandpass_model
synthetic_photometry_model
color_index_model
flux_ratio_model
luminosity_model
bolometric_model
solar_reference_model
extinction_model
reddening_model
atmospheric_extinction_model
K_correction_model
instrumental_magnitude_model
photometric_calibration_model
detector_model
aperture_photometry_model
PSF_photometry_model
saturation_model
variability_model
mean_magnitude_model
binary_blend_model
surface_brightness_distinction_model
spectral_type_context_model
temporal_model
relationships
constraints
measurement_model
uncertainty_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
magnitude_scale_or_zero_point_changes
photometric_system_or_bandpass_changes
distance_modulus_or_extinction_model_changes
bolometric_or_K_correction_model_changes
detector_or_photometric_calibration_changes
variability_or_blending_model_changes
measurement_model_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW