camb: keta_max scaling with lmax at high l

 Posts: 5
 Joined: January 13 2005
 Affiliation: ICE (CSICIEEC) Barcelona
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camb: keta_max scaling with lmax at high l
Hi,
two questions:
while at low l the rule of thumb is that ketamax_scalar should be >~twice lmax_scalar, does this scaling holds for lmax>5000 say? From what I can see it does not, and it goes in the direction of ketamax>2 lmax. Is there a rule of thumb that can be applied in this regime?
(yes I could run convergence tests by gradually increasing k_eta_max, but if somebody has done this already, it'll be very useful....)
Also, up to what lmax is camb safe and tested? what could "go wrong" if one wanted to go at even higer l's (meaning if one wanted to trust the results above lmax)?
It may sound silly, after all secondary CMB starts dominating at l>~5000 or so. But, in a couple of years there will be CMB data up to l=10000. An accurate modeling of secondary effects will require at least some modeling of the primary....
Thnaks.
two questions:
while at low l the rule of thumb is that ketamax_scalar should be >~twice lmax_scalar, does this scaling holds for lmax>5000 say? From what I can see it does not, and it goes in the direction of ketamax>2 lmax. Is there a rule of thumb that can be applied in this regime?
(yes I could run convergence tests by gradually increasing k_eta_max, but if somebody has done this already, it'll be very useful....)
Also, up to what lmax is camb safe and tested? what could "go wrong" if one wanted to go at even higer l's (meaning if one wanted to trust the results above lmax)?
It may sound silly, after all secondary CMB starts dominating at l>~5000 or so. But, in a couple of years there will be CMB data up to l=10000. An accurate modeling of secondary effects will require at least some modeling of the primary....
Thnaks.

 Posts: 1511
 Joined: September 23 2004
 Affiliation: University of Sussex
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Re: camb: keta_max scaling with lmax at high l
The accuracy will depend a bit on what you are calculating (for example the lensed BB is much more sensitive to the maximum k than most other things). I believe it should give reasonable results out to high l, though the accuracy will generally be worse at l>2000 (maybe > percent level; it's not very well tested anyway). At ultra high l you can expect things to screw up, at least without boosting accuracy settings.
For plain unlensed C_l I'd have though the ketamax rule of thumb should be OK.
For plain unlensed C_l I'd have though the ketamax rule of thumb should be OK.

 Posts: 2
 Joined: June 07 2005
 Affiliation: University of Portsmouth
camb: keta_max scaling with lmax at high l
The graph here is a ratio of two models computed using CAMB, where the only difference in parameters or settings between the two is the value of tau (or Z=exp(2 tau)). The effect of this physically results in a constant ratio between the two models. I would like to know if there is a way to extend the accuracy of CAMB at very high l (note the x axis is log scale). The settings include no lensing, scalars only, the accuracy_boost and l_accuracy_boost both set to 2, l_sample_boost is 1, and k_eta_max (20200) is exactly twice l_max_scalar (10100). Could this be a manifestation that the rule k_eta_max_scalar ~ 2 lmax_scalar breaks down at very high l?
Thank you.
Thank you.

 Posts: 1511
 Joined: September 23 2004
 Affiliation: University of Sussex
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Re: camb: keta_max scaling with lmax at high l
Probably not  the problem is that the unlensed CMB is absolutely tiny on these scales so I can image all sorts of numerical problems kick in; though if you want to track down the problem I'd be happy to add in any fix you find...
I would guess this specific problem is related to late time evolution, so may be better calculating with tau=0, then multiplying the small scale spectrum by the appropriate damping factor.
However I don't really see why you want to calculate something that is totally unobservable? (*much* smaller than lensing and kineticSZ/OV on these scales)
There are also problems calculating the lensing potential power spectrum on very small scales. Accuracy boost helps, but ultimately using the Limber approximation would probably be a much better way to go (there's no support for Limber in CAMB at the moment  it always does full spherical calculation which is inefficient on very small scales where Limber is excellent). Note the very small scale lensed CMB only depends on the small scale lensing potential power spectrum, the unlensed CMB is irrelevant on these scales (see e.g. Sec 4 of astroph/0601594).
I would guess this specific problem is related to late time evolution, so may be better calculating with tau=0, then multiplying the small scale spectrum by the appropriate damping factor.
However I don't really see why you want to calculate something that is totally unobservable? (*much* smaller than lensing and kineticSZ/OV on these scales)
There are also problems calculating the lensing potential power spectrum on very small scales. Accuracy boost helps, but ultimately using the Limber approximation would probably be a much better way to go (there's no support for Limber in CAMB at the moment  it always does full spherical calculation which is inefficient on very small scales where Limber is excellent). Note the very small scale lensed CMB only depends on the small scale lensing potential power spectrum, the unlensed CMB is irrelevant on these scales (see e.g. Sec 4 of astroph/0601594).

 Posts: 41
 Joined: November 22 2004
 Affiliation: ITP Heidelberg
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camb: keta_max scaling with lmax at high l
Maybe some sort of accuracy estimate could be given by running CAMB vs both gauges of CMBEASY. They are fairly independent. We could run a "plain" vanilla model with and without reionization and see how much the curves deviate. Btw: if CAMB uses a swift reionization (as CMBFAST and CMBEASY does), then I could imagine that you'll see some deviation like discussed above: this might at the end be physical, not a numerical artefact. But I'm not sure here, we would have to check (see my speedingupthe boltzmanncodepaper on the effect of the swift reionization that the codes use on the photons).
Anyway. We'll compare CAMB vs the two cmbeasy gauges and take a look at the high l values.
Anyway. We'll compare CAMB vs the two cmbeasy gauges and take a look at the high l values.