adding the m12.py model (#148)

* Added two new models

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* Updated 9 and 8 and added another mixed slab model

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* add a uniform slab model 5 has a FR screen in front of it

* fixed slab

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* Made a uniform emission screen model

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* fixed 1a

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* Update m1a.py

fixed 1a

* removed m5a and m1a not needed

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* Create m12.py

* Delete RMtools_1D/models_ns/m9.py

* Delete RMtools_1D/models_ns/m9_1.py

* Delete RMtools_1D/models_ns/m8.py

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---------

Co-authored-by: loberhel <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

RMtools_1D/models_ns/m12.py

@@ -0,0 +1,84 @@
+#
+# =============================================================================#
+import bilby
+import numpy as np
+
+
+# -----------------------------------------------------------------------------#
+# Function defining the model.                                                #
+#                                                                             #
+#  pDict       = Dictionary of parameters, created by parsing inParms, below. #
+#  lamSqArr_m2 = Array of lambda-squared values                               #
+#  quArr       = Complex array containing the Re and Im spectra.              #
+# -----------------------------------------------------------------------------#
+def model(pDict, lamSqArr_m2):
+    """
+    Single Faraday component with internal Faraday dispersion and
+    an foreground external dispersion screen
+
+    Ref:
+    Sokoloff et al. (1998) Eq 34
+    O'Sullivan et al. (2012) Eq 10
+    Oberhelman et al. (in prep) Eq 6
+    """
+
+    # Calculate the complex fractional q and u spectra
+    pArr = pDict["fracPol"] * np.ones_like(lamSqArr_m2)
+    para_S = (
+        2.0 * lamSqArr_m2**2 * pDict["sigmaRM_radm2"] ** 2
+        - 2j * lamSqArr_m2 * pDict["deltaRM_radm2"]
+    )
+
+    quArr = (
+        pArr
+        * np.exp(
+            2j * (np.radians(pDict["psi0_deg"]) + pDict["RM_screen"] * lamSqArr_m2)
+        )
+        * ((1 - np.exp(-1.0 * para_S)) / para_S)
+        * np.exp(-2.0 * pDict["sigmaRM_radm2_FG"] ** 2.0 * lamSqArr_m2**2.0)
+    )
+
+    return quArr
+
+
+# -----------------------------------------------------------------------------#
+# Priors for the above model.                                                 #
+# See https://lscsoft.docs.ligo.org/bilby/prior.html for details.             #
+#                                                                             #
+# -----------------------------------------------------------------------------#
+priors = {
+    "fracPol": bilby.prior.Uniform(
+        minimum=0.0, maximum=0.6, name="fracPol", latex_label="$p$"
+    ),
+    "psi0_deg": bilby.prior.Uniform(
+        minimum=0,
+        maximum=180.0,
+        name="psi0_deg",
+        latex_label="$\psi_0$ (deg)",
+        boundary="periodic",
+    ),
+    "deltaRM_radm2": bilby.prior.Uniform(
+        minimum=0.0,
+        maximum=60.0,
+        name="deltaRM_radm2",
+        latex_label="$\Delta{RM}$ (rad m$^{-2}$)",
+    ),
+    "sigmaRM_radm2": bilby.prior.Uniform(
+        minimum=0.0,
+        maximum=50.0,
+        name="sigmaRM_radm2",
+        latex_label="$\sigma_{RM}$ (rad m$^{-2}$)",
+    ),
+    "sigmaRM_radm2_FG": bilby.prior.Uniform(
+        minimum=0.0,
+        maximum=50.0,
+        name="sigmaRM_radm2_FG",
+        latex_label="$\sigma_{RM,FG}$ (rad m$^{-2}$)",
+    ),
+    "RM_screen": bilby.prior.Uniform(
+        minimum=-1100.0,
+        maximum=1100.0,
+        name="RM_screen_radm2_FG",
+        latex_label="$RM_{screen,FG}$ (rad m$^{-2}$)",
+    ),
+}