### About X-ray luminosities for halos in T300-1

Yaqub Zheng
• 27 Dec '23

For X-ray emission, I compute 0.5-2.0 keV band luminosities using APEC model. We derive the X-ray luminosities of each gas cell based on its density, temperature, and metallicity. We exclude all the gas cells with SFR > 0.

However, my calculation appears to be approximately 0.5 dex higher than the T300-1 results obtained by Nelson+2023 (Fig.10 in arXiv:2311.06338) at the same M500. I'm not quite sure which calculation step went wrong.

The temperature of each gas cell is calculated based on the following page: https://www.tng-project.org/data/docs/faq/#gen6

The code for this section is as follows:

mu_ = 4/(1+3*0.76+4*0.76*halo_gas['ElectronAbundance'])*m_p
temp_ = (2/3*halo_gas['InternalEnergy']/k_B*(1*u.kpc/u.Gyr)**2*mu_).to('K')
temp_keV = (2/3*halo_gas['InternalEnergy']*(1*u.kpc/u.Gyr)**2*mu_).to('keV')


The normalization of the model for each gas cell, assuming the standard prescription of $10^{-14} \int n_e n_p dV/[4 \pi (1+z)^2 D_A^2]$, $z$ is the redshift and conventionally set to $z=0.1$ in a fiducial way.

The code for this is as follows:

norm_ = 1e-14*((halo_gas['ElectronAbundance']*halo_gas['Masses']*halo_gas['Density']*((0.76*1e10*M_sun)**2)/(m_p**2)/(u.kpc)**3)/(4*np.pi*(cos.angular_diameter_distance(0.1)*(1+0.1))**2)).to('cm-5')


Thank you for help!

Best,
Zheng

Dylan Nelson
• 28 Dec '23

Seems reasonable, although I am not sure about all the details of the "normalization". In the plot from Nelson+ you show above, I did not assume any redshift (as luminosity, not flux, is plotted). Does your result depend on redshift?

Yaqub Zheng
• 28 Dec '23

Hi,

I have checked the redshift dependence and found no dependency on it.

The normalization of the model refers to this link: https://hea-www.cfa.harvard.edu/soxs/users_guide/thermal_spectra.html?highlight=thermal#generating-spectra

Dylan Nelson
• 29 Dec '23

Perhaps you could compare against a simple (analytic) bremsstrahlung estimation. I recall that for the massive clusters, the difference with APEC was minimal (i.e. <1%), so this should clarify any issues in the SOXS pipeline.

Yaqub Zheng
• 2 Jan

Hi Dylan,

I simultaneously used the official instructions and the pyXsim package to calculate the X-ray emissions of an arbitrary galaxy cluster.

As shown in the figure below, while my calculations and those from pyXsim are inconsistent, it is evident that they differ by a fixed factor. The factor is about 1.5, but I guess it is 1/h (h=0.6774).

I also checked the gas temperature calculated by the two methods, and they are almost identical, indicating that the issue lies in the calculation of normalization, and it may be related to the Hubble constant.

When calculating the normalization, I defaulted to h = 1. If h is retained without substituting any numerical value, the calculated Lx units are in “h erg/s”.

However, the Lx units in observational studies are typically in "h^-2 erg/s". I guess that the results for Lx in your paper are also in "h^-2 erg/s", rather than the "erg/s" displayed in the Fig.10 in arXiv:2311.06338. If that is the case, multiplying my original calculations by h^3 would scale down the numerical values by 0.5 dex overall, making them similar to your calculations.

Thank you for help!

Dylan Nelson
• 2 Jan

Thanks for tracking down the difference, indeed we must always be careful with factors of h.

(The values shown in Fig. 10 of that paper do not have any h factors. The units are as stated on the axes.).

Yaqub Zheng
• 2 Jan

Wait, if it's not "h^-2 erg/s," does that mean the M500 has also been divided by h?

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