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Hi,
I am trying to draw the surface brightness map within a radius of 1*SubhaloStellarPhotometricsRadius from the galaxies' center
in this process, I want to check the definition of SubhaloStellarPhotometicsRad( drops below the limit of 20.7 mag arcsec−2 in the K band )
so, I wonder about the distance when deciding on this Subhalo Stellar Photometrics Rad.
I'm so sorry if there's a research paper or explanation related to this but I couldn't find it.

Thank you for your help and kind regards

This is using the GFM_StellarPhotometrics[3] values for the K-band, also stored in the snapshots for every star.

If you calculate a radial profile of this field, normalize by the area in arcsec^-2, you should be able to rederive the value of SubhaloStellarPhotometicsRad following the definition you posted above.

Thanks for your reply!
But there's a question.

When i calculated the surface brightness map (mag/arcsec^2) using GFM_Stellar Photometrics (k band,vega magnitude) as follows:

in here, D is physical size(GridSize) per pixel, z is redshift, angular-diameter distance d_A,
alpha is pixel scale, x indicates different filter bands at rest-frame.

so, I think to calculate a given area in arcsec^2, shouldn’t we assume a distance?

Isn't that how we can confirm that when we draw a surface brightness map within 1 * Subhalo Stellar Photometrics Rad, it is filled with values less than 20.7 mag/arcsec^2?

Yes that's correct, you want to convert something like convert luminosity/pc^2 to mag/arcsec^2, including cosmological surface brightness dimming effects corresponding to distance to the redshift of the snapshot.

Just a note though: this value was just computed because we thought it might be useful for something. There is no particular reason you need to use, or compute, this exact value.

I got it ., but I wanted to make sure I was doing something wrong or doing well in calculating surface brightness maps(in k band) with SubhaloPhotometricsRad.

So, it would be really helpful for me if you could tell me what distance you set up and obtained in deriving SubhaloStellarPhotometricRad.

thank you !

Hi Yeongyeong,

The code snippet looks like this:

    GFM_STELLAR_PHOTOMETRICS_K_LIMIT = 20.7   # limiting surface brightness determining 'detectable radius'

            factor1 = 5 * np.log10(3600 * 360 / 10 / 2 / np.pi)
            factor2 = 2.5 * np.log10(np.power(atime * UnitLength_in_cm / PARSEC / HubbleParam, 2))

            # convert luminosity/pc^2 to mag/arcsec^2, including cosmological surface brightness dimming
            if lum > 0:
                tmp_sb = factor1 - 2.5 * np.log10(lum) + \
                         2.5 * np.log10(np.pi * (rad[i]**2 - rad[i]**2)) + \
                         factor2 - 2.5 * np.log10(atime**4)

                if GFM_STELLAR_PHOTOMETRICS_K_LIMIT > tmp_sb:
                    sblim_list_rr[i] = rad_grid[irad + 1]
                    break

        SubhaloStellarPhotometricsRad = sblim_list_rr[   int(np.floor(GFM_STELLAR_PHOTOMETRICS_DIRECTIONS/2)) ]

Hi Dylan,
Thanks so much for your reply.

But there is one more question, I think 'atime' in the code is 1/(1+z), is it right?
If that's right, what is this value of z(redshift)?

I'm not good enough at English.
so, if you must be hard to understand, please tell me (Even if it was a question above).

Thank you for always answering kindly.

Yes atime is the scalefactor for the given redshift. Each snapshot has a different redshift, you can find it in the Header.

For example, snapshot 99 is z=0 for all TNG50/100/300 simulations.

Hello Dylan!,
Thanks for your reply! and sorry for the late reply.
I want to ask you one more question to check because I'm confused.

Namely, do you mean that to derive the SubhaloStellarPhotometricRad, In calculating the SurfaceBrightnessProfile, *the assumed distance to subhalos are respectively z=0,z=0.1, etc. according to snapshot=99,98, etc. ?

*The assumed distance is corresponding to AngularDistance in the expression mentioned above.
(see image below)

Thank you.

Each snapshot is the state of the simulation at a specific redshift. So any calculation involving the age of the universe, the lookback time, the distance, etc, would typically use the redshift of the snapshot.

Dear Dylan,

many thanks for your help.

I'd like to ask you one more thing.
Could you tell me what absolute magnitude (k band) of solar was used to calculate the surface brightness magnitude?

As far as I know, the information about K band is (Buser K filter + Palomar200 IR detectors + atmosphere.57) and Vega magnitude .

I found a filter that I thought was similar to this at the following site(http://mips.as.arizona.edu/~cnaw/sun.html
) and obtained vega magnitude(3.27).

so, Surface Brightness Profile of specific subhalos was obtained as follows, but it was confirmed that the value(22.5 mag/arcsec^2) when it corresponds to a SubhaloStellarPhotometicsradius(Blue line) was about 2 magnitudes darker than the expected value(20.8 mag/arcsec^2).

Since checking all the cases that could be miscalculated, it seems highly likely that the M(sun,k) I used is the wrong value.
Otherwise, the calculation method used is likely to be wrong, but I hope not. Please help me get a clue about it.

Best Regards,
Yeongyeong Lee

You would find these details in the BC03 paper and documentation, since this is what the stellar photometrics are based on.

Dear Dylan,

I want to express my sincere gratitude for your help in resolving the issues I was curious about.
Your kindness and support have been invaluable throughout this process, and I cannot thank you enough for everything you have done.

Best regards,
Yeongyeong Lee