A spectral survey of an ultra-hot Jupiter - Detection of metals in the transmission spectrum of KELT-9 b

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Volume 627 (July 2019)

A&A, 627 (2019) A165

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Table C.2

Coefficients for the fit of the temperature-dependent mass action constants of ions (including anions).

Species	a₀	a₁	b₀	b₁	b₂	Reference
Li⁺	−6.257651e+04	2.445125e+00	−1.458903e+01	6.911880e-05	−9.971750e-09	b
Li²⁺	−9.403432e+05	4.954491e+00	−2.817262e+01	5.864958e-05	−8.710342e-09	b
Li⁻	7.168737e+03	−2.523718e+00	1.366656e+01	3.180655e-05	−5.015196e-09	b
Be⁺	−1.081981e+05	2.448287e+00	−1.320213e+01	4.864945e-05	−5.720544e-09	a
Be²⁺	−3.195220e+05	4.969213e+00	−2.825779e+01	3.688612e-05	−4.907970e-09	b
B⁺	−9.628053e+04	2.499047e+00	−1.600591e+01	7.692046e-07	−9.594323e-11	a
B²⁺	−3.195039e+05	4.996323e+00	−2.951576e+01	2.978475e-06	−3.149719e-10	a
B⁻	3.222835e+03	−2.486416e+00	1.454006e+01	−1.579851e-05	3.089472e-09	a
C²⁺	−4.135903e+05	4.984436e+00	−3.053864e+01	1.684809e-05	−3.164118e-09	a
N²⁺	−5.122099e+05	5.230785e+00	−2.965536e+01	−1.073986e-04	6.073966e-09	a
O²⁺	−5.656110e+05	5.242922e+00	−3.012987e+01	−1.230956e-04	8.130114e-09	a
F²⁺	−6.080289e+05	4.758626e+00	−2.708094e+01	9.538401e-05	−5.702377e-09	a
Ne²⁺	−7.255567e+05	5.331451e+00	−2.883738e+01	−8.033248e-05	3.091043e-09	a
Na²⁺	−6.083678e+05	4.994249e+00	−2.778162e+01	1.569849e-04	−1.785986e-08	a
Mg²⁺	−2.632132e+05	4.967207e+00	−2.824584e+01	3.926133e-05	−5.215984e-09	a
Al²⁺	−2.879089e+05	4.883613e+00	−2.873766e+01	6.361646e-05	−4.708568e-09	a
Si²⁺	−2.841943e+05	4.782967e+00	−2.910203e+01	1.008866e-04	−1.017122e-08	a
P²⁺	−3.510207e+05	5.702043e+00	−3.321286e+01	−2.354251e-04	6.150734e-09	a
S²⁺	−3.910012e+05	5.789528e+00	−3.409596e+01	−3.487582e-04	2.160394e-08	a
Cl²⁺	−4.268605e+05	4.843548e+00	−2.745382e+01	−1.815412e-05	5.086697e-09	a
Ar²⁺	−5.034790e+05	5.165356e+00	−2.791532e+01	5.757654e-05	−6.291260e-09	a
K²⁺	−4.174481e+05	4.800569e+00	−2.660964e+01	3.187530e-04	−3.631262e-08	a
Ca²⁺	−2.087315e+05	4.826088e+00	−2.741512e+01	2.233377e-04	−3.281908e-08	a
Ca⁻	2.491226e+02	−2.330029e+00	1.530053e+01	−6.796035e-05	5.088252e-09	a
Sc⁺	−7.630457e+04	1.939671e+00	−1.029001e+01	5.553202e-04	−4.992972e-08	c
Sc²⁺	−2.246849e+05	4.929991e+00	−2.810383e+01	1.530566e-04	−2.843184e-08	a
Sc⁻	2.178975e+03	−2.360998e+00	1.380622e+01	2.356529e-05	5.089711e-10	a
Ti²⁺	−2.367560e+05	5.084696e+00	−2.902846e+01	−1.698708e-05	−1.619924e-08	a
V²⁺	−2.484095e+05	5.040063e+00	−2.863070e+01	−1.905291e-04	8.702925e-09	a
Cr²⁺	−2.698671e+05	5.771943e+00	−3.258554e+01	−3.510903e-04	5.252151e-09	a
Mn²⁺	−2.677758e+05	4.913883e+00	−2.793082e+01	1.069395e-04	−1.499061e-08	a
Fe²⁺	−2.795485e+05	5.019119e+00	−2.859377e+01	1.347711e-05	−1.155154e-08	a
Co²⁺	−2.896757e+05	5.142486e+00	−2.926769e+01	−2.023968e-04	9.480268e-09	a
Ni²⁺	−2.995070e+05	4.693818e+00	−2.697957e+01	1.608813e-04	−1.118022e-08	a
Cu²⁺	−3.251517e+05	4.903999e+00	−2.684981e+01	2.482547e-04	−2.988537e-08	a
Zn²⁺	−3.174840e+05	4.996642e+00	−2.842085e+01	3.752581e-06	−4.509092e-10	a
Ga⁺	−6.980530e+04	1.607740e+00	−9.320869e+00	3.015434e-04	−1.633885e-08	b
Ga²⁺	−3.077803e+05	4.331296e+00	−2.435889e+01	1.712459e-04	−6.810332e-09	b
Ga⁻	5.057817e+03	−1.891447e+00	1.006145e+01	−2.051303e-04	1.451311e-08	b
Ge⁺	−9.176634e+04	1.425826e+00	−7.483645e+00	5.963214e-04	−4.297209e-08	b
Ge²⁺	−2.767541e+05	3.722745e+00	−2.089299e+01	3.763743e-04	−2.132323e-08	b
Ge⁻	1.413645e+04	−3.747478e+00	2.298821e+01	3.220351e-04	−9.528489e-09	b
As⁺	−1.132523e+05	3.756197e+00	−2.390343e+01	−1.167552e-04	−8.836227e-09	b
As²⁺	−3.298491e+05	4.732759e+00	−2.765064e+01	4.718120e-04	−4.177260e-08	b
As⁻	9.334082e+03	−2.584351e+00	1.486495e+01	2.373549e-04	−2.365011e-08	b
Se⁺	−1.131779e+05	2.554645e+00	−1.466664e+01	−2.114424e-04	1.839430e-08	b
Se²⁺	−3.590378e+05	5.062661e+00	−3.069360e+01	4.448638e-04	−3.987156e-08	b
Se⁻	2.343896e+04	−2.524085e+00	1.420115e+01	−8.135546e-05	6.462952e-09	b
Rb⁺	−4.854618e+04	2.197062e+00	−1.301519e+01	2.942980e-04	−3.670703e-08	b
Rb²⁺	−3.651322e+05	4.808020e+00	−2.660509e+01	2.284562e-04	−2.926039e-08	b
Rb⁻	5.642096e+03	−2.471924e+00	1.337032e+01	−4.960086e-05	9.617959e-09	b
Sr⁺	−6.614589e+04	2.245360e+00	−1.194103e+01	2.583965e-04	−3.380599e-08	a
Sr²⁺	−1.941161e+05	4.792835e+00	−2.722238e+01	2.716941e-04	−4.104279e-08	b
Sr⁻	6.627934e+02	−1.992876e+00	1.269203e+01	−1.370573e-04	4.628944e-09	a
Y⁺	−7.176276e+04	4.188361e+00	−2.641749e+01	−4.324053e-04	7.814626e-09	a
Y²⁺	−2.141923e+05	4.843393e+00	−2.767314e+01	2.539009e-04	−3.793062e-08	b
Y⁻	3.556755e+03	−2.634410e+00	1.507707e+01	4.561236e-04	−3.724981e-08	a
Zr⁺	−7.701333e+04	2.627948e+00	−1.484642e+01	3.778927e-05	−1.404338e-08	a
Zr²⁺	−2.293259e+05	5.104568e+00	−2.914197e+01	−1.287425e-04	−5.281367e-09	a
Zr⁻	5.029101e+03	−2.350380e+00	1.428294e+01	−1.913007e-04	8.780821e-09	a
Nb⁺	−7.857835e+04	2.612763e+00	−1.580872e+01	1.123904e-04	−1.049845e-08	a
Nb²⁺	−2.445578e+05	5.211120e+00	−3.088235e+01	−3.620478e-05	−5.447194e-09	a
Nb⁻	1.058498e+04	−3.066374e+00	1.704201e+01	−8.271939e-05	2.007041e-08	a
Mo⁺	−8.230749e+04	2.489498e+00	−1.430508e+01	6.234623e-06	−4.526990e-10	a
Mo²⁺	−2.697311e+05	6.302578e+00	−3.729495e+01	−2.766927e-04	−3.447993e-09	a
Mo⁻	8.620377e+03	−2.969326e+00	1.665969e+01	8.507653e-04	−7.317276e-08	a
Ru⁺	−8.543378e+04	2.412469e+00	−1.375638e+01	6.152285e-07	−3.017937e-09	a
Ru²⁺	−2.798820e+05	5.157276e+00	−2.959099e+01	−1.427370e-04	6.698495e-11	a
Ru⁻	1.211661e+04	−2.677755e+00	1.518654e+01	1.408877e-04	−1.581984e-08	a
Rh⁺	−8.660251e+04	2.382664e+00	−1.346571e+01	−9.551840e-05	7.588277e-09	a
Rh²⁺	−2.963766e+05	4.971467e+00	−2.820594e+01	−1.055777e-04	7.448432e-09	a
Rh⁻	1.317054e+04	−2.981142e+00	1.499211e+01	1.587576e-04	1.303818e-08	a
Pd⁺	−9.650404e+04	3.427600e+00	−1.837233e+01	−6.848823e-04	2.286147e-08	a
Pd²⁺	−3.221492e+05	5.425302e+00	−2.885909e+01	−3.406978e-04	1.232565e-09	a
Pd⁻	6.619238e+03	−1.901975e+00	1.129693e+01	−5.718141e-04	1.219657e-08	a
Ag⁺	−8.791960e+04	2.494306e+00	−1.487763e+01	5.114261e-06	−5.635751e-10	b
Ag²⁺	−3.373123e+05	4.913882e+00	−2.683080e+01	9.621756e-05	−3.857636e-09	b
Ag⁻	1.513778e+04	−2.499833e+00	1.352636e+01	−1.864851e-07	2.239051e-11	b
Cd⁺	−1.043706e+05	2.492493e+00	−1.347983e+01	6.696760e-06	−7.311102e-10	b
Cd²⁺	−3.005824e+05	4.995789e+00	−2.841579e+01	4.798662e-06	−5.945109e-10	b
In⁺	−6.720764e+04	2.430559e+00	−1.421171e+01	−2.867153e-04	2.412735e-08	b
In²⁺	−2.861252e+05	5.086195e+00	−2.879086e+01	−3.773571e-04	3.074917e-08	b
In⁻	4.494223e+03	−2.363480e+00	1.250462e+01	2.701248e-04	−2.307383e-08	b
Sn⁺	−8.550616e+04	1.636183e+00	−7.583424e+00	−9.394052e-06	1.328952e-08	b
Sn²⁺	−2.550640e+05	4.949683e+00	−2.776817e+01	−6.474905e-04	5.382399e-08	b
Sn⁻	1.286251e+04	−2.549000e+00	1.628734e+01	−6.778121e-04	6.572371e-08	b
Sb⁺	−9.999992e+04	1.861317e+00	−1.187724e+01	8.992890e-04	−6.835289e-08	b
Sb²⁺	−2.917412e+05	4.893050e+00	−2.849750e+01	1.207286e-04	−9.306244e-09	b
Sb⁻	1.214207e+04	−2.590659e+00	1.497120e+01	1.213584e-04	−1.205327e-08	b
Te⁺	−1.048358e+05	1.636178e+00	−7.583391e+00	−9.390886e-06	1.328928e-08	b
Te²⁺	−3.204477e+05	4.659802e+00	−2.802328e+01	3.713875e-04	−1.538476e-08	b
Te⁻	2.288286e+04	−2.421080e+00	1.352850e+01	−8.725159e-05	2.439641e-09	b
Cs⁺	−4.528316e+04	2.087691e+00	−1.234395e+01	4.185307e-04	−5.552924e-08	b
Cs²⁺	−3.139541e+05	4.755044e+00	−2.630289e+01	3.156288e-04	−4.718043e-08	b
Cs⁻	5.399787e+03	−2.931135e+00	1.617382e+01	3.635188e-04	−4.840012e-09	b
Ba⁺	−6.051156e+04	2.230065e+00	−1.201430e+01	4.601799e-04	−6.798839e-08	b
Ba²⁺	−1.765336e+05	5.179498e+00	−2.960346e+01	−3.866059e-05	−4.383653e-08	b
Ba⁻	1.750082e+03	−2.233250e+00	1.365346e+01	4.925290e-04	−7.194586e-08	b
La⁺	−6.451483e+04	3.326088e+00	−1.927360e+01	−4.769959e-04	1.819639e-08	b
La²⁺	−1.930757e+05	4.975852e+00	−2.818165e+01	−2.888187e-04	1.285448e-08	b
La⁻	6.348587e+03	−2.654876e+00	1.605691e+01	4.380221e-04	−3.161517e-08	b
Ce⁺	−6.403419e+04	3.171264e+00	−1.914062e+01	−1.056822e-04	−1.019987e-08	b
Ce²⁺	−1.902176e+05	4.699222e+00	−2.673118e+01	−1.068922e-04	1.316049e-09	b
Ce⁻	6.548959e+03	−2.955035e+00	1.702923e+01	−3.701637e-05	2.383397e-08	b
Pr⁺	−6.342175e+04	3.126189e+00	−1.798169e+01	−2.761204e-04	3.578332e-09	b
Pr²⁺	−1.858490e+05	5.582066e+00	−3.192867e+01	−6.136215e-04	2.352541e-08	b
Pr⁻	1.122440e+04	−2.082943e+00	1.164134e+01	−4.125150e-04	3.774982e-08	b
Nd⁺	−6.403886e+04	2.975283e+00	−1.718373e+01	−7.720646e-05	−1.314762e-08	b
Nd²⁺	−1.885906e+05	5.217612e+00	−2.981865e+01	−1.050506e-04	−3.399976e-08	b
Nd⁻	2.230139e+04	−2.102172e+00	1.134207e+01	−7.139634e-05	−3.701865e-08	b
Sm⁺	−6.547008e+04	2.282160e+00	−1.268932e+01	3.636024e-04	−3.906499e-08	b
Sm²⁺	−1.939742e+05	4.842841e+00	−2.753764e+01	2.379702e-04	−4.274995e-08	b
Sm⁻	1.758414e+03	−3.749298e+00	2.321110e+01	5.770456e-05	7.703514e-09	b
Eu⁺	−6.581677e+04	2.345689e+00	−1.328486e+01	3.752787e-04	−4.408329e-08	b
Eu²⁺	−1.962769e+05	4.799913e+00	−2.727418e+01	2.795278e-04	−4.568226e-08	b
Eu⁻	1.388057e+03	−1.804402e+00	1.017602e+01	−7.181045e-06	−5.833591e-09	b
Gd⁺	−7.137337e+04	2.276964e+00	−1.300354e+01	4.336840e-04	−4.546894e-08	b
Gd²⁺	−2.116502e+05	4.932654e+00	−2.835878e+01	2.831846e-04	−4.332661e-08	b
Gd⁻	1.546839e+03	−2.916868e+00	1.763578e+01	3.829147e-04	−3.072644e-08	b
Tb⁺	−6.799838e+04	2.010817e+00	−1.204494e+01	5.350978e-04	−4.895898e-08	b
Tb²⁺	−2.018045e+05	4.200660e+00	−2.406078e+01	2.802467e-04	−1.396694e-08	b
Tb⁻	1.348067e+04	−3.028296e+00	1.710919e+01	−1.334802e-04	3.541371e-08	b
Dy⁺	−6.879472e+04	3.014676e+00	−1.747181e+01	−1.157870e-04	−1.117657e-08	b
Dy²⁺	−2.043326e+05	5.041662e+00	−2.873304e+01	4.613373e-05	−4.562549e-08	b
Dy⁻	4.084086e+03	−2.493290e+00	1.413667e+01	−2.962651e-05	7.644436e-10	b
Ho⁺	−6.977167e+04	2.996212e+00	−1.728031e+01	−8.020657e-05	−2.656349e-08	b
Ho²⁺	−2.068032e+05	5.015257e+00	−2.857871e+01	6.703620e-05	−3.148431e-08	b
Ho⁻	3.906039e+03	−2.604632e+00	1.464065e+01	1.087372e-04	−5.276441e-09	b
Er⁺	−7.078944e+04	3.047784e+00	−1.739668e+01	−2.387930e-04	−1.836723e-09	b
Er²⁺	−2.093003e+05	5.089075e+00	−2.902460e+01	−3.946951e-06	−3.000136e-08	b
Er⁻	3.682983e+03	−2.119010e+00	1.141914e+01	−3.518785e-04	8.140888e-09	b
Tm⁺	−7.184576e+04	2.426255e+00	−1.322566e+01	1.704652e-04	−2.721242e-08	b
Tm²⁺	−2.116323e+05	4.782511e+00	−2.715946e+01	2.813775e-04	−4.166156e-08	b
Tm⁻	1.193280e+04	−2.565770e+00	1.251438e+01	1.095083e-04	−2.155381e-08	b
Yb⁺	−7.262584e+04	2.296951e+00	−1.225092e+01	1.917634e-04	−2.271257e-08	b
Yb²⁺	−2.138997e+05	4.833709e+00	−2.745114e+01	1.989037e-04	−2.642820e-08	b
Lu⁺	−6.300162e+04	2.540992e+00	−1.557599e+01	−4.279115e-04	5.199291e-08	b
Lu²⁺	−2.243108e+05	4.820128e+00	−2.789396e+01	−9.521387e-05	1.856125e-08	b
Lu⁻	3.973630e+03	−2.756844e+00	1.600575e+01	2.107913e-04	−5.906525e-09	b
Hf⁺	−7.928592e+04	2.161891e+00	−1.229210e+01	2.526805e-04	−1.769312e-08	b
Hf²⁺	−2.520756e+05	5.292591e+00	−3.007134e+01	−5.024157e-04	2.303820e-08	b
Hf⁻	2.062321e+03	−2.547061e+00	1.423421e+01	1.360278e-04	−5.484156e-09	b
Ta⁺	−8.744604e+04	3.158873e+00	−1.877288e+01	−1.554275e-04	−1.253218e-09	b
Ta²⁺	−2.755660e+05	5.339651e+00	−3.030819e+01	−6.384433e-04	2.852234e-08	b
Ta⁻	3.847936e+03	−2.093770e+00	9.994987e+00	3.261281e-04	−4.536083e-08	b
W⁺	−9.150081e+04	1.776468e+00	−8.550768e+00	8.439088e-05	7.391207e-09	b
W²⁺	−2.813461e+05	4.382890e+00	−2.444833e+01	7.191376e-05	1.445050e-08	b
W⁻	9.432156e+03	−2.405402e+00	1.604370e+01	−1.189007e-03	1.106563e-07	b
Re⁺	−9.091879e+04	2.421065e+00	−1.359550e+01	1.070258e-04	−1.897499e-08	b
Re²⁺	−2.835463e+05	4.945248e+00	−2.812904e+01	8.913961e-05	−1.714456e-08	b
Re⁻	6.391571e+02	−2.938058e+00	1.718643e+01	5.689440e-04	−4.466452e-08	b
Os⁺	−9.790556e+04	2.578877e+00	−1.459216e+01	−9.155119e-05	2.202461e-09	b
Os²⁺	−2.951961e+05	5.019104e+00	−2.854965e+01	−2.882173e-05	−4.096798e-09	b
Os⁻	1.251071e+04	−2.487400e+00	1.423524e+01	1.393521e-05	−5.261997e-09	b
Ir⁺	−1.040089e+05	2.669729e+00	−1.524435e+01	−7.712863e-05	2.059896e-09	b
Ir²⁺	−3.012993e+05	5.264280e+00	−2.997023e+01	−3.584437e-04	1.315339e-08	b
Ir⁻	1.829105e+04	−1.568548e+00	8.278251e+00	−5.396383e-04	2.501637e-08	b
Pt⁺	−1.042118e+05	1.320760e+00	−7.001288e+00	5.594756e-04	−2.525852e-08	b
Pt²⁺	−3.194780e+05	4.332828e+00	−2.413334e+01	1.811947e-04	−1.186298e-08	b
Pt⁻	2.455609e+04	−3.174591e+00	1.708680e+01	1.556494e-04	1.006783e-09	b
Au⁺	−1.070045e+05	2.707671e+00	−1.623589e+01	−1.701164e-04	1.276849e-08	b
Au²⁺	−3.449473e+05	5.007420e+00	−2.740510e+01	2.554497e-05	−1.286974e-08	b
Au⁻	2.679326e+04	−2.492163e+00	1.346216e+01	2.508001e-05	−1.281389e-08	b
Hg⁺	−1.211222e+05	2.500164e+00	−1.352840e+01	−1.513729e-07	1.719679e-11	b
Hg²⁺	−3.387766e+05	4.999857e+00	−2.844015e+01	1.615884e-07	−1.969555e-11	b
Tl⁺	−7.085577e+04	2.594299e+00	−1.553214e+01	−4.979836e-05	−5.224852e-09	b
Tl²⁺	−3.079320e+05	5.042748e+00	−2.871117e+01	−1.973543e-05	−7.424893e-09	b
Tl⁻	4.366684e+03	−2.538768e+00	1.378263e+01	5.992629e-07	1.267056e-08	b
Pb⁺	−8.599945e+04	2.735546e+00	−1.507083e+01	−1.299813e-04	−9.032662e-09	b
Pb²⁺	−2.604921e+05	5.081516e+00	−2.896644e+01	−2.033514e-05	−2.009540e-08	b
Pb⁻	4.160111e+03	−2.388659e+00	1.490846e+01	−6.395885e-05	−1.246717e-08	b
Bi⁺	−8.452993e+04	2.569671e+00	−1.603952e+01	−7.216128e-05	9.600723e-09	b
Bi²⁺	−2.782281e+05	4.979024e+00	−2.901385e+01	3.292111e-05	−6.184604e-09	b
Bi⁻	1.093209e+04	−2.525123e+00	1.459062e+01	3.398221e-05	−5.099485e-09	b
Th⁺	−7.304474e+04	2.979942e+00	−1.767323e+01	−2.152028e-05	−1.087038e-08	b
Th²⁺	−2.066111e+05	5.368242e+00	−2.958683e+01	−2.757084e-04	−1.065319e-09	b
U⁺	−7.187899e+04	2.500000e+00	−1.448287e+01	−1.221136e-11	9.189032e-16	b
U²⁺	−2.064914e+05	5.000000e+00	−2.880874e+01	−3.535195e-15	2.891645e-19	b

Notes.The fits are valid in the temperature range between 100 and 6000 K and are given in the FastChem format: (Stock et al. 2018). References. a: partition functions based on data from the Kurucz line lists (Kurucz & Bell 1995). b: partition functions based on data from the NIST Atomic Spectra Database (Kramida et al. 2018b). The ionization energies are taken from the Lide (2004) in both cases. c: based on thermochemical data from Gurvich et al. (1982).

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