How to compute counts (photons/sec) for an H-Alpha emission diffuse object?

[dan_adi]

Lately I was reviewing the math for my exposure time calculator. Everything works out fine for broad-band imaging, but I am stuck on narrowband.

With broad-band, in Vega - Mag system every Mag/Flux is normalized to Vega. If we take a random 18 V Mag star we can simply compute the flux as, 

F = 10^(-0.4 * m) * F0, where F0 is the 0 point flux for the V band. Further we divide the flux to the photon energy and we get the counts.

But what about a H-alpha emission nebula? We don't have H-Alpha magnitudes, and we don't have 0 point fluxes.

I did find an example in the HST handbook, see the attached screenshot. In the example the flux is provided, but how? Do I search Vizier and get the flux for the object? After I find the flux don't I have to normalized it somehow? 

 

[dan_adi]

Made a little progress ... 

Here we have a database with H alpha fluxes: http://vizier.cds.unistra.fr/viz-bin/VizieR-3?-source=J/MNRAS/431/2/fluxes

Also the article that discusses the theory:  https://academic.oup.com/mnras/article/431/1/2/1036908

On pg. 12 in the pdf "...
with the exception of McCullough et al. (2001) who
determined a flux for Abell 36 of F(Hα) = 2.8 × 10−11 erg cm−2 s−1,
which is 28 per cent lower than our own determination of 3.9 ×
10−11 erg cm−2 s−1."

If I look up Abell 36 in their database I find a logF = -10.41 mW/m^2

Playing with the code:

import numpy as np
from scipy.integrate import simps

# Given logFlux in mW/m²
logFlux_mW_per_m2 = -10.41

# Convert logFlux to regular flux in mW/m²
flux_mW_per_m2 = 10 ** logFlux_mW_per_m2

# Load filter transmission data from file (assuming two columns: wavelength, transmission)
filter_data = np.loadtxt('H-alpha-3nm_2.txt')
wavelengths = filter_data[:, 0]  # Wavelengths in Ångströms
transmission_values = filter_data[:, 1]  # Filter transmission values

# Interpolate the filter transmission data to match the flux wavelengths (if needed)
# Assuming the filter and flux data have matching wavelengths

# Calculate the product of flux and filter transmission
flux_times_transmission = flux_mW_per_m2 * transmission_values

# Integrate the product over the wavelength range to get erg/s/cm²
erg_per_s_per_cm2 = simps(flux_times_transmission, wavelengths)

# Convert the result to erg/s/cm²/Å by dividing by the bandwidth (in Ångströms)

erg_per_s_per_cm2_per_Angstrom = erg_per_s_per_cm2 / 30 #bandwidth_Angstrom

print("Flux in erg/s/cm²/Å:", erg_per_s_per_cm2_per_Angstrom)

The result is : 

Flux in erg/s/cm²/Å: 3.90462998411593e-11

So I think this is the way to convert the vizier flux data to flux density in H-alpha since the values is identical to the one in the article.

In order to compute the counts we divide this flux density by the photon energy at 656.3 nm.

Now all I need is to compute  the sky brightness from a H-alpha fits file in ASTAP, the result being in mag/arcsec^2. 

Then convert that mag to h-alpha flux (based on the article data), and finally, hopefully compute a correct exposure time in narrowband.

This is much harder than BVRI imaging, all because there is no standard "magnitude" system for narrowband