def lsst_flare_fluxes_from_u(ju_flux):
"""
Convert from Johnson U band flux to flux in the LSST bands
by assuming the flare is a 9000K black body (see Section 4
of Hawley et al 2003, ApJ 597, 535)
Parameters
----------
flux in Johnson U band (either a float or a numpy array)
Returns
-------
floats/numpy arrays of fluxes in all 6 LSST bands
"""
if not hasattr(lsst_flare_fluxes_from_u, 'johnson_u_raw_flux'):
t_start = time.time()
throughputs_dir = getPackageDir('throughputs')
johnson_dir = os.path.join(throughputs_dir, 'johnson')
johnson_u_hw = Bandpass()
johnson_u_hw.readThroughput(os.path.join(johnson_dir, 'johnson_U.dat'))
atm = Bandpass()
atm.readThroughput(
os.path.join(throughputs_dir, 'baseline', 'atmos_std.dat'))
wv, sb = johnson_u_hw.multiplyThroughputs(atm.wavelen, atm.sb)
johnson_u = Bandpass(wavelen=wv, sb=sb)
boltzmann_k = 1.3807e-16 # erg/K
planck_h = 6.6261e-27 # erg*s
_c = 2.9979e10 # cm/s
hc_over_k = 1.4387e7 # nm*K
temp = 9000.0 # black body temperature in Kelvin
bb_wavelen = np.arange(200.0, 1500.0, 0.1) # in nanometers
exp_arg = hc_over_k / (temp * bb_wavelen)
exp_term = 1.0 / (np.exp(exp_arg) - 1.0)
ln_exp_term = np.log(exp_term)
# the -7.0 np.log(10) will convert wavelen into centimeters
log_bb_flambda = -5.0 * (np.log(bb_wavelen) -
7.0 * np.log(10.0)) + ln_exp_term
log_bb_flambda += np.log(2.0) + np.log(planck_h) + 2.0 * np.log(_c)
# assume these stars all have radii half that of the Sun;
# see Boyajian et al. 2012 (ApJ 757, 112)
r_sun = 6.957e10 # cm
log_bb_flambda += np.log(
4.0 * np.pi * np.pi) + 2.0 * np.log(0.5 * r_sun)
# thee -7.0*np.log(10.0) makes sure we get ergs/s/cm^2/nm
bb_flambda = np.exp(log_bb_flambda - 7.0 * np.log(10))
bb_sed = Sed(wavelen=bb_wavelen, flambda=bb_flambda)
# because we have a flux in ergs/s but need a flux in
# the normalized units of Sed.calcFlux (see eqn 2.1
# of the LSST Science Book), we will calculate the
# ergs/s/cm^2 of a raw, unnormalized blackbody spectrum
# in the Johnson U band, find the factor that converts
# that raw flux into our specified flux, and then
# multiply that factor *by the fluxes calculated for the
# blackbody in the LSST filters using Sed.calcFlux()*.
# This should give us the correct normalized flux for
# the flares in the LSST filters.
lsst_flare_fluxes_from_u.johnson_u_raw_flux = bb_sed.calcErgs(
johnson_u)
lsst_bands = BandpassDict.loadTotalBandpassesFromFiles()
norm_raw = None
lsst_flare_fluxes_from_u.lsst_raw_flux_dict = {}
for band_name in ('u', 'g', 'r', 'i', 'z', 'y'):
bp = lsst_bands[band_name]
flux = bb_sed.calcFlux(bp)
lsst_flare_fluxes_from_u.lsst_raw_flux_dict[band_name] = flux
if norm_raw is None:
norm_raw = flux
print('raw flux in %s = %e; %e; %e' %
(band_name, flux, flux / norm_raw, bb_sed.calcErgs(bp)))
print('sed johnson flux %e' %
lsst_flare_fluxes_from_u.johnson_u_raw_flux)
print('that init took %e' % (time.time() - t_start))
factor = ju_flux / lsst_flare_fluxes_from_u.johnson_u_raw_flux
u_flux_out = factor * lsst_flare_fluxes_from_u.lsst_raw_flux_dict['u']
g_flux_out = factor * lsst_flare_fluxes_from_u.lsst_raw_flux_dict['g']
r_flux_out = factor * lsst_flare_fluxes_from_u.lsst_raw_flux_dict['r']
i_flux_out = factor * lsst_flare_fluxes_from_u.lsst_raw_flux_dict['i']
z_flux_out = factor * lsst_flare_fluxes_from_u.lsst_raw_flux_dict['z']
y_flux_out = factor * lsst_flare_fluxes_from_u.lsst_raw_flux_dict['y']
return (u_flux_out, g_flux_out, r_flux_out, i_flux_out, z_flux_out,
y_flux_out)
def test_calcErgs(self):
"""
Test that calcErgs actually calculates the flux of a source in
ergs/s/cm^2 by running it on black bodies with flat bandpasses
and comparing to the Stefan-Boltzmann law.
"""
boltzmann_k = 1.3807e-16 # in ergs/Kelvin
planck_h = 6.6261e-27 # in cm^2*g/s
speed_of_light = 2.9979e10 # in cm/s
stefan_boltzmann_sigma = 5.6705e-5 # in ergs/cm^2/s/Kelvin
wavelen_arr = np.arange(10.0, 200000.0, 10.0) # in nm
bp = Bandpass(wavelen=wavelen_arr, sb=np.ones(len(wavelen_arr)))
log10_bb_factor = np.log10(2.0) + np.log10(planck_h)
log10_bb_factor += 2.0*np.log10(speed_of_light)
log10_bb_factor -= 5.0*(np.log10(wavelen_arr) - 7.0) # convert wavelen to cm
for temp in np.arange(5000.0, 7000.0, 250.0):
log10_exp_arg = np.log10(planck_h) + np.log10(speed_of_light)
log10_exp_arg -= (np.log10(wavelen_arr) - 7.0)
log10_exp_arg -= (np.log10(boltzmann_k) + np.log10(temp))
exp_arg = np.power(10.0, log10_exp_arg)
log10_bose_factor = -1.0*np.log10(np.exp(exp_arg)-1.0)
# the -7.0 below is because, otherwise, flambda will be in
# ergs/s/cm^2/cm and we want ergs/s/cm^2/nm
#
# the np.pi comes from the integral in the 'Stefan-Boltzmann'
# section of
# https://en.wikipedia.org/wiki/Planck%27s_law#Stefan.E2.80.93Boltzmann_law
#
bb_flambda = np.pi*np.power(10.0, log10_bb_factor+log10_bose_factor-7.0)
sed = Sed(wavelen=wavelen_arr, flambda=bb_flambda)
ergs = sed.calcErgs(bp)
log10_ergs = np.log10(stefan_boltzmann_sigma) + 4.0*np.log10(temp)
ergs_truth = np.power(10.0, log10_ergs)
msg = '\ntemp:%e\nergs: %e\nergs_truth: %e' % (temp, ergs, ergs_truth)
self.assertAlmostEqual(ergs/ergs_truth, 1.0, 3, msg=msg)
# Now test it on a bandpass with throughput=0.25 and an wavelength
# array that is not the same as the SED
wavelen_arr = np.arange(10.0, 100000.0, 146.0) # in nm
bp = Bandpass(wavelen=wavelen_arr, sb=0.25*np.ones(len(wavelen_arr)))
wavelen_arr = np.arange(5.0, 200000.0, 17.0)
log10_bb_factor = np.log10(2.0) + np.log10(planck_h)
log10_bb_factor += 2.0*np.log10(speed_of_light)
log10_bb_factor -= 5.0*(np.log10(wavelen_arr) - 7.0) # convert wavelen to cm
for temp in np.arange(5000.0, 7000.0, 250.0):
log10_exp_arg = np.log10(planck_h) + np.log10(speed_of_light)
log10_exp_arg -= (np.log10(wavelen_arr) - 7.0)
log10_exp_arg -= (np.log10(boltzmann_k) + np.log10(temp))
exp_arg = np.power(10.0, log10_exp_arg)
log10_bose_factor = -1.0*np.log10(np.exp(exp_arg)-1.0)
# the -7.0 below is because, otherwise, flambda will be in
# ergs/s/cm^2/cm and we want ergs/s/cm^2/nm
#
# the np.pi comes from the integral in the 'Stefan-Boltzmann'
# section of
# https://en.wikipedia.org/wiki/Planck%27s_law#Stefan.E2.80.93Boltzmann_law
#
bb_flambda = np.pi*np.power(10.0, log10_bb_factor+log10_bose_factor-7.0)
sed = Sed(wavelen=wavelen_arr, flambda=bb_flambda)
ergs = sed.calcErgs(bp)
log10_ergs = np.log10(stefan_boltzmann_sigma) + 4.0*np.log10(temp)
ergs_truth = np.power(10.0, log10_ergs)
msg = '\ntemp: %e\nergs: %e\nergs_truth: %e' % (temp,ergs, ergs_truth)
self.assertAlmostEqual(ergs/ergs_truth, 0.25, 3, msg=msg)
def test_calcErgs(self):
"""
Test that calcErgs actually calculates the flux of a source in
ergs/s/cm^2 by running it on black bodies with flat bandpasses
and comparing to the Stefan-Boltzmann law.
"""
boltzmann_k = 1.3807e-16 # in ergs/Kelvin
planck_h = 6.6261e-27 # in cm^2*g/s
speed_of_light = 2.9979e10 # in cm/s
stefan_boltzmann_sigma = 5.6705e-5 # in ergs/cm^2/s/Kelvin
wavelen_arr = np.arange(10.0, 200000.0, 10.0) # in nm
bp = Bandpass(wavelen=wavelen_arr, sb=np.ones(len(wavelen_arr)))
log10_bb_factor = np.log10(2.0) + np.log10(planck_h)
log10_bb_factor += 2.0 * np.log10(speed_of_light)
log10_bb_factor -= 5.0 * (np.log10(wavelen_arr) - 7.0
) # convert wavelen to cm
for temp in np.arange(5000.0, 7000.0, 250.0):
log10_exp_arg = np.log10(planck_h) + np.log10(speed_of_light)
log10_exp_arg -= (np.log10(wavelen_arr) - 7.0)
log10_exp_arg -= (np.log10(boltzmann_k) + np.log10(temp))
exp_arg = np.power(10.0, log10_exp_arg)
log10_bose_factor = -1.0 * np.log10(np.exp(exp_arg) - 1.0)
# the -7.0 below is because, otherwise, flambda will be in
# ergs/s/cm^2/cm and we want ergs/s/cm^2/nm
#
# the np.pi comes from the integral in the 'Stefan-Boltzmann'
# section of
# https://en.wikipedia.org/wiki/Planck%27s_law#Stefan.E2.80.93Boltzmann_law
#
bb_flambda = np.pi * np.power(
10.0, log10_bb_factor + log10_bose_factor - 7.0)
sed = Sed(wavelen=wavelen_arr, flambda=bb_flambda)
ergs = sed.calcErgs(bp)
log10_ergs = np.log10(
stefan_boltzmann_sigma) + 4.0 * np.log10(temp)
ergs_truth = np.power(10.0, log10_ergs)
msg = '\ntemp:%e\nergs: %e\nergs_truth: %e' % (temp, ergs,
ergs_truth)
self.assertAlmostEqual(ergs / ergs_truth, 1.0, 3, msg=msg)
# Now test it on a bandpass with throughput=0.25 and an wavelength
# array that is not the same as the SED
wavelen_arr = np.arange(10.0, 100000.0, 146.0) # in nm
bp = Bandpass(wavelen=wavelen_arr, sb=0.25 * np.ones(len(wavelen_arr)))
wavelen_arr = np.arange(5.0, 200000.0, 17.0)
log10_bb_factor = np.log10(2.0) + np.log10(planck_h)
log10_bb_factor += 2.0 * np.log10(speed_of_light)
log10_bb_factor -= 5.0 * (np.log10(wavelen_arr) - 7.0
) # convert wavelen to cm
for temp in np.arange(5000.0, 7000.0, 250.0):
log10_exp_arg = np.log10(planck_h) + np.log10(speed_of_light)
log10_exp_arg -= (np.log10(wavelen_arr) - 7.0)
log10_exp_arg -= (np.log10(boltzmann_k) + np.log10(temp))
exp_arg = np.power(10.0, log10_exp_arg)
log10_bose_factor = -1.0 * np.log10(np.exp(exp_arg) - 1.0)
# the -7.0 below is because, otherwise, flambda will be in
# ergs/s/cm^2/cm and we want ergs/s/cm^2/nm
#
# the np.pi comes from the integral in the 'Stefan-Boltzmann'
# section of
# https://en.wikipedia.org/wiki/Planck%27s_law#Stefan.E2.80.93Boltzmann_law
#
bb_flambda = np.pi * np.power(
10.0, log10_bb_factor + log10_bose_factor - 7.0)
sed = Sed(wavelen=wavelen_arr, flambda=bb_flambda)
ergs = sed.calcErgs(bp)
log10_ergs = np.log10(
stefan_boltzmann_sigma) + 4.0 * np.log10(temp)
ergs_truth = np.power(10.0, log10_ergs)
msg = '\ntemp: %e\nergs: %e\nergs_truth: %e' % (temp, ergs,
ergs_truth)
self.assertAlmostEqual(ergs / ergs_truth, 0.25, 3, msg=msg)
