Usage

>>> from cosmolopy import magnitudes
>>> nu = magnitudes.nu_lambda(1216.)
>>> lam = magnitudes.nu_lambda(nu)
>>> lam
1216.0

Usage

>>> from cosmolopy import magnitudes
>>> fnu, nu = magnitudes.f_nu_lambda(2.0, 1216.)
>>> flam, lam = magnitudes.f_nu_lambda(fnu, nu)
>>> flam, lam
(2.0, 1216.0)

Usage

Check that the AB magnitude zero point is 3631 Jy:

>>> from cosmolopy import magnitudes
>>> "%.4g" % (magnitudes.f_nu_from_magAB(0.0)/1e-23)
'3631'

Usage

Check that the AB magnitude zero point is 3631 Jy:

>>> from cosmolopy import magnitudes
>>> import math
>>> L_nu = magnitudes.L_nu_from_magAB(0.0)
>>> "%.4g" % (L_nu/(1e-23 * 4. * math.pi * (10*cc.pc_cm)**2))
'3631'

Usage

Check that the AB magnitude zero point is 3631 Jy:

>>> import numpy, math
>>> from cosmolopy import magnitudes, cc
>>> L_nu = 3631e-23 * (4. * math.pi * (10*cc.pc_cm)**2)
>>> "%.3f" % numpy.abs(magnitudes.magnitude_AB_from_L_nu(L_nu))
'0.000'

Usage

>>> from cosmolopy import fidcosmo, magnitudes
>>> "mu(z=6) = %.4g" % magnitudes.distance_modulus(6.0, **fidcosmo)
'mu(z=6) = 48.86'

Inputs

z: array or scalar

the redshift of the source. Set to None to get absolute magnitude from a luminosity.

f_lambda: array or scalar

observed flux from the source in units of erg s^-1 cm^-2 Ang^-1

wavelength: array or scalar

the observed wavelength of the flux measurement(s) in Angstroms

Returns

Returns ab (apparent), and AB (absolute) magnitudes.

Notes

Note that here you pass fluxes that are per unit wavelength, not per unit frequency. To get the absolute magnitude for a luminosity specified in units of erg s^-1 Ang^-1, set z=None.

Usage

Check that the AB magnitude zero point is 3631 Jy:

>>> from cosmolopy import fidcosmo, magnitudes, cc, cd
>>> import numpy, math
>>> L_nu = 3631e-23 * (4. * math.pi * (10*cc.pc_cm)**2)
>>> nu = magnitudes.nu_lambda(1216.)
>>> L_lambda, lamb = magnitudes.f_nu_lambda(L_nu, nu)
>>> mAB, MAB = magnitudes.magnitude_AB(None, L_lambda, 1216., **fidcosmo)
>>> "%.3f" % numpy.abs(MAB)
'0.000'

Find the apparent (and absolute, which should be zero) magnitudes of a 3631 Jy source at z=6.0:

>>> from cosmolopy import fidcosmo, magnitudes, cc, cd
>>> import numpy, math
>>> L_nu = 3631e-23 * (4. * math.pi * (10*cc.pc_cm)**2)
>>> nu = magnitudes.nu_lambda(1216.)
>>> L_lambda, lamb = magnitudes.f_nu_lambda(L_nu, nu)
>>> dl = cd.luminosity_distance(6.0, **fidcosmo)
>>> f_lambda = L_lambda/(4. * math.pi * (dl*cc.Mpc_cm)**2 * (1. + 6.0))
>>> mAB, MAB = magnitudes.magnitude_AB(6.0, f_lambda, 7.*1216., **fidcosmo)
>>> "%.3f, %.3f" % (mAB, MAB)
'48.865, 0.000'

Inputs

z: array or scalar

the redshift of the source

f_lambda: array or scalar

observed flux from the source in units of erg s^-1 cm^-2 Ang^-1

wavelength: array or scalar

the observed wavelength of the flux measurement(s) in Angstroms.

nu_power:

the powerlaw index (f_nu ~ nu^nu_power) used to extrapolate the flux to 1450 Angstroms.

Returns

Apparent and absolute magnitudes extrapolated to 1450 Angstroms.

Notes

Follows Fan et al. 2003:

We extrapolate the continuum to rest-frame 1450A, assuming a continuum shape f_nu ~ nu^-0.5 to calculate AB_1450.

Usage

Find the apparent and absolute rest-frame 1450 Angstrom magnitudes of source with a flux of 3631 Jy at rest-frame 1216 Angstroms at z=6.0:

>>> from cosmolopy import fidcosmo, magnitudes, cc, cd
>>> import numpy, math
>>> L_nu = 3631e-23 * (4. * math.pi * (10*cc.pc_cm)**2)
>>> nu = magnitudes.nu_lambda(1216.)
>>> L_lambda, lamb = magnitudes.f_nu_lambda(L_nu, nu)
>>> dl = cd.luminosity_distance(6.0, **fidcosmo)
>>> f_lambda = L_lambda/(4. * math.pi * (dl*cc.Mpc_cm)**2 * (1. + 6.0))
>>> mAB, MAB = magnitudes.magnitude_AB1450(6.0, f_lambda, 7.*1216.,
...                                        **fidcosmo)
>>> "%.3f, %.3f" % (mAB, MAB)
'48.769, -0.096'

And is that offset from an absolute magnitude of zero consisten with our assumed powerlaw index?

>>> "%.3f" %(-2.5 * numpy.log10((1216./1450)**0.5))
'0.096'