The second data release from the European Pulsar Timing Array - IV. Implications for massive black holes, dark matter, and the early Universe

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Volume 685 (May 2024)

A&A, 685 (2024) A94

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Table 1.

Parameters used for the search and their respective priors.

Parameter	Description	Prior	Occurrence
White noise $(σ = E_{f}^{2} σ_{ToA}^{2} + E_{q}^{2})$ $\left(\sigma = E_f^2 \sigma^2_{\rm ToA} + E_q^2\right)$

E_f	EFAC per backend/receiver system	Uniform [0, 10]	1 per pulsar
E_q	EQUAD per backend/receiver system	Log₁₀-Uniform [ − 10, −5]	1 per pulsar

Red noise

A_red	Red noise power-law amplitude	Log₁₀-Uniform [ − 20, −6]	1 per pulsar
γ_red	Red noise power-law spectral index	Uniform [0, 10]	1 per pulsar

ULDM

Ψ_c	ULDM amplitude	Log₁₀-Uniform [ − 20, −12]	1 for PTA
m_ϕ [eV]	ULDM mass	Log₁₀-Uniform [ − 24, −22]	1 for PTA
${\hat{ϕ}}_{E}^{2}$ $\hat{\phi}_{\mathrm{E}}^2$	Earth factor	e^−x	1 for PTA
${\hat{ϕ}}_{P}^{2}$ $\hat{\phi}_{\mathrm{P}}^2$	Pulsar factor	e^−x	1 per pulsar
γ_E	Earth signal phase	Uniform [0, 2π]	1 per PTA
γ_P	Pulsar signal phase	Uniform [0, 2π]	1 per pulsar

Common spatially Uncorrelated Red Noise (CURN)

A_GWB	Common process strain amplitude	Log₁₀-Uniform [ − 20, −6]	1 for PTA

Notes. In the correlated limit, ${\hat{ϕ}}_{E}^{2} = {\hat{ϕ}}_{P}^{2}$ $\hat{\phi}^2_{\mathrm{E}} = \hat{\phi}^2_{\mathrm{P}}$ and can be reabsorbed in a redefinition of Ψ_c.

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