Modelling of surface brightness fluctuation measurements - Methodology, uncertainty, and recommendations

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Volume 686 (June 2024)

A&A, 686 (2024) A62

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Table B.1.

Glossary.

L	Integrated light of the galaxy.
m	Apparent magnitude of the galaxy.

$\bar{m}$ ${\bar{m}}$	SBF magnitude of the galaxy.

R_eff	Effective radius of the galaxy.

I_eff	Intensity per unit area at the effective radius of the galaxy.

n	Sersic index.

b_n	Indicator of the Sersic profile shape (2n - 0.324).

μ_eff	Surface brightness at the effective radius.

N_Reff	Number of counts at the effective radius.

PHOT_C0	Nominal camera zero point (CFHT/MegaCam).

t_exp	Exposure time in seconds.

N_Sky	Sky background counts.

n_pix	Size of the image in number of pixels.

σ_PSF	Standard deviation of the PSF, a 2-D Gaussian in our work.

n_mask pix	Number of pixels within a mask.

N(Gal_mean)	Count number from any pixel of Gal_mean.

$\bar{N}$ $\bar{N}$	Number of counts associated with the SBF. If present, a subscript indicates the source of the $\bar{N}$ $\bar{N}$ value.

σ_fluc	Standard deviation of the fluctuation of the stellar population.

${\bar{N}}_{⟨ SBF ⟩}$ $\bar{N}_{\langle\mathrm{SBF} \rangle}$	Pixel-weighted average of the variable SBFs found in the studied region of the galaxy.

Rand_Gauss	Randomisation of a given value following a normal (Gaussian) distribution.

Rand_Poi	Randomisation of a given value following a Poisson distribution.

Gal_mean	Reference image of the galaxy (as the following, size n_pix × n_pix), here calculated with a Sersic profile.

Gal_fluc	Image with the fluctuation due to the stellar population.

Gal_mean, fluc	Reference image of the galaxy including the fluctuation of the stellar population.

Gal_{mean, fluc, sky}	Image of the galaxy including the fluctuation of the stellar population, plus the sky background.

Gal_{mean, fluc, sky, PSF}	Image of the galaxy including the fluctuation of the stellar population, plus the sky background,
	convolved with the PSF.

Gal_mock	Image of the mock galaxy, built as the mean reference galaxy with the fluctuation, plus the
	sky background, convolved with the PSF, plus a Poisson randomisation as instrumental noise.

Gal_{mock fluc mask}	Normalised image of the fluctuation due to the stellar population and the instrumental noise.

Sky	Image of the sky, with constant value N_Sky.

PSF	Image of the point spread function.

R	Image of the instrumental noise.

R_approx	Image of the modelled instrumental noise.

norm (superindex)	Normalised, i.e. divided by $\sqrt{{Gal}_{mean} \otimes PSF}$ $\sqrt{{\mathrm{Gal}_{\mathrm{mean}}}\otimes \mathrm{PSF}}$ .

Mask	Image of the mask as zero-one (false-true) pixels.

PS	Power spectrum image.

r (subindex)	Azimuthally averaged.

k	Frequency in the Fourier space.

[k_fit, i, k_fit, i]	Range of frequencies within which the fitting is performed.

ε_rel	Relative error of the measurement, calculated as $\| {\bar{N}}_{real} - {\bar{N}}_{fit} \| / {\bar{N}}_{real}$ $\|\bar{N}_{\mathrm{real}}-\bar{N}_{\mathrm{fit}}\|/\bar{N}_{\mathrm{real}}$ .

σ_fit	Relative standard deviation of the fitting.

ε_rel, 90%	Higher 90% percentile of the distribution of ε_rel values.

σ_fit, 90%	Higher 90% percentile of the distribution of σ_fit values.

Δ90%	Relative 90% width of the ${\bar{N}}_{fit}$ $\bar{N}_{\mathrm{fit}}$ distribution.

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