Variation of impact range, energy range and viewcone with zenith.

[moralejo]

Based on general scaling arguments (evolution of the air mass as ~1/cos(zenith) in the planar atmosphere approximation), one can obtain an approximate variation of the MC production parameters.

• E-range limits would scale as 1 / cos^2 zenith (i.e. like the inverse of the light density at fixed energy)
• Max Impact would scale as 1 / cos zenith (i.e. like the light pool radius)
• Viewcone:
  • for diffuse gammas: no scaling (neither in the training, nor in the testing sample) we will not generally need IRFs beyond, say, 2.5 degrees off-axis (and if needed for an exceptional event, it is better to make a dedicated production).
  • for diffuse protons (training only): same scaling as the maximum impact? See tests below with existing MC.

The above scaling of the energy range does not account for the effect of absorption. @jsitarek, based on experience from MAGIC, suggested to modify the E-range as 1 / cos^2.5 zenith

If for diffuse gammas we start with 5GeV - 50 TeV and 1000 m max impact at ZD ~ 0, this would result in 73 GeV - 730 TeV and 2923 m at ZD=70 degrees. But we should clip the upper edge at, say, 200 TeV, since we don't need IRFs (at least urgently) at such huge energies, and it would consume a lot of the computing time.

For the diffuse protons for the training we could start at low zenith with 1000 m, 10 GeV - 100 TeV, and 8 deg. Since this is just for training, there is no need to have a "complete" sample (i.e. one containing ~ all protons that may possibly trigger the telescope). The scaling could be the same as explained above for gammas, clipping the upper energy to 400 TeV. Such set-up might perhaps be too costly at high zenith, this is something to be checked.

[moralejo]

Tests using the existing proton productions

(impact is w.r.t. LST1, properly calculated taking into account the pointing & the LST1 z-coordinate).

ZD = 20 degree, south-wise:

ZD = 60 degree, south-wise:

[moralejo]

Same thing as above with the 20 and 60 deg existing productions of diffuse gammas.

But here I impose a maximum off-axis angle of 2.5 degrees (blue histograms), since we are mostly interested in sources well within our field of view. And then a cut on 0.5 degrees (orange histograms) to evaluate the point-like wobble case.

ZD = 20 degree, south-wise:

ZD = 60 degree, south-wise:

[moralejo]

Based on the plots above, and considering that LST1 is ~70 m from the array center and has larger reach in impact, FOV and energy than MAGIC, I propose the settings below. For NSCAT (shower re-use) I would keep 10 in all cases, like in the previous production.

- Diffuse protons:

• Viewcone: 8 degree at ZD=0, scaling as cos^0.5 ZD. This becomes 5.65 deg at ZD=60. This is purely empirical, it is not clear to me why the needed maximum angle becomes smaller at larger zenith.

• Energy range: 10 GeV - 100 TeV at ZD=0, Scale as cos^-2.5 ZD, but clipping Emax at 200 TeV. This means 57 GeV to 200 TeV at ZD= 60 deg.

• Maximum impact: 1500 m at ZD=0, scaling as cos^-0.5 ZD, i.e. 2121 m at ZD=60 deg. The naïve scaling with cos^-1 would result in way too large max impact (3000 m) at 60 deg zenith

- Diffuse gammas:

• Viewcone 0 - 2.5 deg, independent of zenith (performance beyond that is not relevant in general)
• Energy range: 5 GeV - 50 TeV at ZD=0. Scale as cos^-2.5 ZD, but clipping Emax at 200 TeV. This means 28 GeV to 200 TeV at ZD = 60 deg. This seems very reasonable looking at the plots above (where Emin=100 GeV seems clearly too high for 60 deg)
• Maximum impact: 900 m at ZD=0, scaling as cos^-0.5 ZD, i.e. 1273 m at ZD=60 deg. The naïve scaling with cos^-1 ZD would result in way too large max impact (1800 m) at 60 deg zenith

- Point-like (wobble 0.4) gammas:

• Viewcone: 0.3999 - 0.4001, i.e. "ring wobble", to better represent actual observations
• Energy range: 5 GeV - 50 TeV at ZD=0. Scale as cos^-2.5 ZD, but clipping Emax at 200 TeV. This means 28 GeV to 200 TeV at ZD = 60 deg.
• Maximum impact: 700 m at ZD=0, scale as cos^-1 ZD (1400 m at ZD=60 deg). Not clear to me why here the naïve scaling ~cos^-1 ZD seems to work better than for the diffuse gammas up to 2.5 deg.

[Voutsi]

Tests using the existing proton productions

(impact is w.r.t. LST1, properly calculated taking into account the pointing & the LST1 z-coordinate).

ZD = 20 degree, south-wise:

[...]

Just for clarification, these plots show simulated protons, triggered protons or protons that will pass analysis cuts?

[moralejo]

Just for clarification, these plots show simulated protons, triggered protons or protons that will pass analysis cuts?

This is after cleaning, note the intensity cuts.

[rlopezcoto]

what is the maximum simulated impact for zd 20 and 60 deg? do you have an explanation for the impact scaling with cos^-0.5 ZD instead of cos^-1 ZD? In any case the proposal for the simulation settings sounds good.

[jsitarek]

@moralejo , did you make also dedicated plots for point-like gammas, or just using the diffuse ones <0.5 deg offset?

What is rather striking to me is that for gammas at 2.5 deg we still have very good acceptance from the plots of Abelardo. I think we might consider to increase it a bit more to ~3 deg. The main reason would be not really to study sources at 2.5+ deg offset, but to have more complete sample, and hence less bias e.g. in head/tail discrimination of the images. Gammas, even diffuse, are still cheaper to produce than protons.

About the strange impact dependence, what were the values in the simulations that you are using? One should be careful with intepreting the drops of the impact distribution, since the centre of the array is shifted with the telescope if you have a sharp cutoff in the simulations it shows as a soft cutoff in the impact distribution, that can be misinterpretted as actual physical cutoff. The offset distribution is also heavily correlated with the impact distribution, this can produce some extra effects.

About the narrowing of the proton viewcone with zenith, this might be an artificial effect due to zenith dependence of the collection area. If you are at low zenith, it does not matter much if you got 5 deg off one way or another, the showers still look similar. But if you are at 60 deg, and you got -5 deg in zenith, you end up with slightly lower threshold at 55 deg, but +5 deg you already have a much larger effect at 65 deg. So I think the net effect would be that at higher zeniths the distribution will seem narrower. I think a safer solution would be to use the same viewcone for protons, no matter what is the zenith.

[moralejo]

what is the maximum simulated impact for zd 20 and 60 deg?

If you mean for the existing simulations, it was 1000 for gammas 1500 m for protons at 20 deg (don't know for 60).

Do you have an explanation for the impact scaling with cos-0.5 ZD instead of cos-1 ZD? In any case the proposal for the simulation settings sounds good.

No, I don't. The naïve scaling works well for gammas, which are actually easier to understand than protons. These are anyway rough estimates, just to avoid wasting too much CPU. And note also that this is just for the training, and we will not have anyway a "complete" sample (e.g. all the heavier nuclei are not there).

[moralejo]

@moralejo , did you make also dedicated plots for point-like gammas, or just using the diffuse ones <0.5 deg offset?

Just the <0.5 deg - we want to produce "ring wobble" anyway.

What is rather striking to me is that for gammas at 2.5 deg we still have very good acceptance from the plots of Abelardo. I think we might consider to increase it a bit more to ~3 deg. The main reason would be not really to study sources at 2.5+ deg offset, but to have more complete sample, and hence less bias e.g. in head/tail discrimination of the images. Gammas, even diffuse, are still cheaper to produce than protons.

So, only for the training sample, right?

About the strange impact dependence, what were the values in the simulations that you are using? One should be careful with intepreting the drops of the impact distribution, since the centre of the array is shifted with the telescope if you have a sharp cutoff in the simulations it shows as a soft cutoff in the impact distribution, that can be misinterpretted as actual physical cutoff. The offset distribution is also heavily correlated with the impact distribution, this can produce some extra effects.

Very good points indeed, and I think this is probably very relevant here. For protons it was 1500 m at 20 deg, and I think 2000 m at 60 deg (@YoshikiOhtani can confirm). So the "cutoffs" we see may well be the ones on the production. On the other hand, I was including all images including those clipped by the FOV edge... with some cut on e.g. CoG position many of the most distant showers will be removed (depending on off-axis angle). To be tested.

About the narrowing of the proton viewcone with zenith, this might be an artificial effect due to zenith dependence of the collection area. If you are at low zenith, it does not matter much if you got 5 deg off one way or another, the showers still look similar. But if you are at 60 deg, and you got -5 deg in zenith, you end up with slightly lower threshold at 55 deg, but +5 deg you already have a much larger effect at 65 deg. So I think the net effect would be that at higher zeniths the distribution will seem narrower. I think a safer solution would be to use the same viewcone for protons, no matter what is the zenith.

Sounds like a promising hypothesis... I can try to check the viewcone thing depending on the direction.

Thanks!

[jsitarek]

Hi,

What is rather striking to me is that for gammas at 2.5 deg we still have

very good acceptance from the plots of Abelardo. I think we might consider to increase it a bit more to ~3 deg. The main reason would be not really to study sources at 2.5+ deg offset, but to have more complete sample, and hence less bias e.g. in head/tail discrimination of the images. Gammas, even diffuse, are still cheaper to produce than protons.

So, only for the training sample, right?

at this stage I think yes. one could still need it in test samples in likelihood methods, but this is pretty special application so we can save some simulation time keeping 2.5 deg for test sample

Cheers, Julian

About the strange impact dependence, what were the values in the simulations that you are using? One should be careful with intepreting the drops of the impact distribution, since the centre of the array is shifted with the telescope if you have a sharp cutoff in the simulations it shows as a soft cutoff in the impact distribution, that can be misinterpretted as actual physical cutoff. The offset distribution is also heavily correlated with the impact distribution, this can produce some extra effects.

Very good points indeed, and I think this is probably very relevant here. For protons it was 1500 m at 20 deg, and I think 2000 m at 60 deg ( @YoshikiOhtani https://github.com/YoshikiOhtani can confirm). So the "cutoffs" we see may well be the ones on the production. On the other hand, I was including all images including those clipped by the FOV edge... with some cut on e.g. CoG position many of the most distant showers will be removed (depending on off-axis angle). To be tested.

About the narrowing of the proton viewcone with zenith, this might be an artificial effect due to zenith dependence of the collection area. If you are at low zenith, it does not matter much if you got 5 deg off one way or another, the showers still look similar. But if you are at 60 deg, and you got -5 deg in zenith, you end up with slightly lower threshold at 55 deg, but +5 deg you already have a much larger effect at 65 deg. So I think the net effect would be that at higher zeniths the distribution will seem narrower. I think a safer solution would be to use the same viewcone for protons, no matter what is the zenith.

Sounds a promising hypothesis... I can try to check the viewcone thing depending on the direction.

Thanks!

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[moralejo]

What is rather striking to me is that for gammas at 2.5 deg we still have very good acceptance from the plots of Abelardo. I think we might consider to increase it a bit more to ~3 deg. The main reason would be not really to study sources at 2.5+ deg offset, but to have more complete sample, and hence less bias e.g. in head/tail discrimination of the images. Gammas, even diffuse, are still cheaper to produce than protons.

Coming back to that, it is not so striking because 2.5 deg is the actual optical FoV radius (a bit less if aberrations are considered), so a large fraction of showers (those "on the right side") coming from that off axis angle will be well within the FoV, even fully contained in many cases. I think however that those will be quite irrelevant for the bulk of the analyses we have to carry out (sources at 0.4 deg offset) , so I would keep it at 2.5. If needed one can produce later a complementary sample at larger offset and merge it.

About the strange impact dependence, what were the values in the simulations that you are using? One should be careful with intepreting the drops of the impact distribution, since the centre of the array is shifted with the telescope if you have a sharp cutoff in the simulations it shows as a soft cutoff in the impact distribution, that can be misinterpretted as actual physical cutoff. The offset distribution is also heavily correlated with the impact distribution, this can produce some extra effects.

Indeed, this is happening in the plots above. For protons at 60 deg, this is the distribution of cores, around the "center of the array" in the MC production, not around the telescope, on the plane orthogonal to the particle momentum, with no intensity cut (I am actually not sure why it is not really a perfect circle with the production radius of 1800 m, may be that the core distribution is done by Corsika for the original primary trajectory, but then it can be modified by the magnetic field? Anyway, not so relevant now):

The corresponding distribution of impact parameters w.r.t. the array center:

Clearly the drop is due to the production limit. Still, we only need the protons for the training, and they are anyway just a part of the actual background, so we can probably ignore the very-large impact protons for the time being.

[moralejo]

About the narrowing of the proton viewcone with zenith, this might be an artificial effect due to zenith dependence of the collection area. If you are at low zenith, it does not matter much if you got 5 deg off one way or another, the showers still look similar. But if you are at 60 deg, and you got -5 deg in zenith, you end up with slightly lower threshold at 55 deg, but +5 deg you already have a much larger effect at 65 deg. So I think the net effect would be that at higher zeniths the distribution will seem narrower. I think a safer solution would be to use the same viewcone for protons, no matter what is the zenith.

Does not seem a big effect. Just one example, the 60 deg protons, intensity>300 pe, I separated between showers with altitude larger and smaller than that of the telescope pointing (orange and green respectively):

Again, since protons are just for training, I think we can save quite some computing time by reducing viewcone with increasing zenith, according to the empirical cos^0.5 ZD scaling proposed above. In case of need, a complementary sample could be produced with larger offsets.

[jsitarek]

@moralejo the part about not a perfect circle: the correction for the magnetic field is there in Corsika, so indeed it can be the case. If it is the dominant reason and you make the distribution let's say above a few TeV it should get much more roundish.

a second possibility is the viewcone. I think that the impact scattering is done w.r.t. the shower axis, while you make the final plot w.r.t. telescope axis, and hence there can be a bit of difference

[moralejo]

a second possibility is the viewcone. I think that the impact scattering is done w.r.t. the shower axis, while you make the final plot w.r.t. telescope axis, and hence there can be a bit of difference

No, not the telescope: events are projected on a plane orthogonal to each shower's direction mc_az, mc_alt

[moralejo]

@moralejo the part about not a perfect circle: the correction for the magnetic field is there in Corsika, so indeed it can be the case. If it is the dominant reason and you make the distribution let's say above a few TeV it should get much more roundish.

Above 30 TeV, does not seem to become more round: At these angles, though, and for such large impacts, all other things (like direction) being equal, there is a large difference in distance from the telescope to the shower between the case in which the core is north or south of the telescope (here showers come from ~south), so lack of symmetry may be normal. I don't know though why cores get further than 1800 m.

[moralejo]

I suggest to start the Corsika production with the scalings proposed in https://github.com/cta-observatory/lst-sim-config/issues/3#issuecomment-993470789, with the grid points (train and test) needed for testing everything on Crab Nebula observations. I will produce a list of pointings with the energy and viewcone limits and open a new issue with that.

[jsitarek]

a second possibility is the viewcone. I think that the impact scattering is done w.r.t. the shower axis, while you make the final plot w.r.t. telescope axis, and hence there can be a bit of difference

No, not the telescope: events are projected on a plane orthogonal to each shower's direction mc_az, mc_alt

ah, sorry, I've read wrongly what you wrote above. But then maybe Corsika does it the other way around (scattering impacts around the original direction), would be a bit strange, but possible. Can you test it, it is a very simple check (just plot it w.r.t. telescope axis instead)?

[moralejo]

ah, sorry, I've read wrongly what you wrote above. But then maybe Corsika does it the other way around (scattering impacts around the original direction), would be a bit strange, but possible. Can you test it, it is a very simple check (just plot it w.r.t. telescope axis instead)?

The manual says the scattering is done in the plane perpendicular to the shower axis. I had anyway tried projecting with the telescope pointing (sorry cannot produce the plot right now) and it did not work either. I might also have some issue with my code, but cannot put more time into this in short term - anyway it is not a key point for deciding on the production settings, so we can defer it.

[maxnoe]

It should be perfectly round when using the tilted ground frame with the pointing direction.

[moralejo]

The manual says shower direction (not the pointing one). It is a bit more symmetric when using the pointing direction, but not circular either - elongated in the N-S direction:

I cannot exclude a software problem, but as I said, I'll park this issue for now since it is not critical for the discussion.

[jsitarek]

thank you for checking. Are you sure that the X axis in the plot is N-S? (in Corsika it should be, but maybe sim_telarray does something funny). The remaining effect looks like GF effect (slight shift and asymmetry), but this one should be in W-E direction. Nevertheless, I agree with you, the effect is minor enough not to cause problems for this production (but if we do not understand it now likely we will not make an effort to do it ever ;-) ).

[moralejo]

x should be the x of the array, which is like the one of Corsika but rotated by the ARRANG angle, which is the magnetic declination. So I think x is geographic north, and y is geographic west.