*** Contamination of the local-form fNL due to the lensing-linear Integrated Sachs-Wolfe effect bispectrum or the lensing-non-linear Rees-Sciama effect bispectrum ***
April 9, 2012: E.Komatsu
Refs: Junk & Komatsu, arXiv:TBD

Here we provide a program for computing a contamination of the local-form fNL due to the lensing-linear Integrated Sachs-Wolfe effect bispectrum or the lensing-non-linear Rees-Sciama effect bispectrum for a full-sky, cosmic-variance only experiment. 

The contamination is computed as

fNL(contamination) = NUM / DENOM

where 

NUM = sum_{2<=l1<=l2<=l3} [B_localform(l1,l2,l3)*B_lensingISW(l1,l2,l3)]
                          /[C(l1)C(l2)C(l3)Delta(l1,l2,l3)]

DENOM = sum_{2<=l1<=l2<=l3} [B_localform(l1,l2,l3)]^2
                            /[C(l1)C(l2)C(l3)Delta(l1,l2,l3)]

<< CAUTION >>
Note that the covariance of the bispectrum appearing in the denominator of the above equation ignores contributions from the non-Gaussian signal (i.e., this covarianec is valid only when non-Gaussianity is absent). This may affect the value of fNL(contamination) at l>~2200. For details, see Lewis, Challinor & Hanson, JCAP, 03, 018 (2011).

In order to compute the local-form bispectrum, B_localform(l1,l2,l3), the code reads in alpha_l(r) and beta_l(r) ("l_r_alpha_beta_lmax=3000.txt"). These data were calculated from the "compute_alphabeta" code, which is also available on Cosmology Routine Library. 

In order to compute the lensing-ISW and lensing-RS bispectra, the code reads in the lensing-ISW and lensing-RS cross-power spectra, Q(l), as well as the power spectrum of the UNLENSED, primordial CMB, Cp(l). We provide the data for the ISW Q(l), "ell_ql_linear.txt", for the RS Q(l), "ell_ql_3pt.txt", computed from the 3rd-order perturbation theory, and for the unlensed C(l), "wmap5baosn_max_likelihood_scalCls.dat". The codes for generating Q(l) are also available on CRL. 

To calculate the variance of the bispectrum (i.e., the denominator of the above equation), we need the lensed C(l), which is included here as "wmap5baosn_max_likelihood_lensedCls.dat".

These data were generatedfor the maximum likelihood parameters given in Table I of Komatsu et al.(2008) [WMAP 5-year interpretation paper] with "WMAP5+BAO+SN". The input file for CAMB is also provided (wmap5baosn_max_likelihood_params.ini). 
- To compile and use the  program, edit Makefile and simply "make"
- It will generate an executable called "compute_fNLcontamination_lensingisw"
- Run "./compute_fNLcontamination_lensingisw", which will generate a data file 
"lmax_fNLcont_linear_nonlinear.txt", which contains:

(1st column) maximum multipole, lmax
(2nd column) fNL(contamination) from the lensing-linear ISW bispectrum
(3rd columm) fNL(contamination) from the lensing-non-linear RS bispectrum

For your convenience, the result of the calculation using the WMAP5+BAO+SN parameters is included as "results/lmax_fNLcont_linear_nonlinear.txt".