Þ¥bonds€¬cell_resultsŠÙ$3ec7c8d3-e5d3-4c7a-ba3c-e0a267131469Š¦queued¤logs§running¦output†¤bodyÛO¤¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚŸmNš¢°persist_js_state·has_pluto_hook_features§cell_idÙ$3ec7c8d3-e5d3-4c7a-ba3c-e0a267131469¹depends_on_disabled_cells§runtimeΰx]µpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$072bddde-dece-4d9f-990b-e374038ba7e6Š¦queued¤logs§running¦output†¤bodyÙT

Raw data for M-Z fit

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚŸ\a5;°persist_js_state·has_pluto_hook_features§cell_idÙ$072bddde-dece-4d9f-990b-e374038ba7e6¹depends_on_disabled_cells§runtimeÎMiµpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$8bd4f390-591f-11ec-0b66-6585ca602debŠ¦queued¤logs§running¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚŸcèðpersist_js_state·has_pluto_hook_features§cell_idÙ$8bd4f390-591f-11ec-0b66-6585ca602deb¹depends_on_disabled_cells§runtimeÎë+jyµpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$bc031ef8-6fa2-4feb-a354-000960395686Š¦queued¤logs§running¦output†¤bodyÚ¶

Fits

M-Z relation:

$12 + \log(O / H) = Z_0 + \log\!\left[1 - \exp\!\left(-\left[\dfrac{M_\star}{M_0}\right]^{\!\gamma}\right)\right]$

In this model, $Z_0$ is the saturation metallicity. It quantifies the asymptotic upper metallicity limit. $M_0$ is the characteristic turnover mass above which the metallicity asymptotically approaches the upper metallicity limit, $Z_0$. At stellar masses $< M_0$, the M-Z relation reduces to a power law with an index $\gamma$.

M-redshift relation:

$\log(M_0 / M_⊙) = a + b \, \log(1 + z)$

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Zahid et al. (2014)

Data

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Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...ªnbpkg_syncÚž Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...®DelimitedFilesÚž Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...ªDataFramesÚž Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...¦ColorsÚž Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...¬LaTeXStringsÚž Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...¬MeasurementsÚž Resolving... ===  Project No packages added to or removed from `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Project.toml`  Updating `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sdwqutsfkd/Manifest.toml` [f43a241f] ↑ Downloads v1.6.0 ⇒ v1.7.0 [44cfe95a] ↑ Pkg v1.12.0 ⇒ v1.12.1 [deac9b47] ↑ LibCURL_jll v8.11.1+1 ⇒ v8.15.0+0 [14a3606d] ↑ MozillaCACerts_jll v2025.5.20 ⇒ v2025.11.4 [458c3c95] ↑ OpenSSL_jll v3.5.1+0 ⇒ v3.5.4+0 [3f19e933] ↑ p7zip_jll v17.5.0+2 ⇒ v17.7.0+0 Instantiating... === Precompiling... === Waiting for notebook process to start... Done. Starting precompilation...§enabled÷restart_recommended_msgÀ´restart_required_msgÀ­busy_packages¶waiting_for_permissionÂÙ,waiting_for_permission_but_probably_disabled«cell_inputsŠÙ$3ec7c8d3-e5d3-4c7a-ba3c-e0a267131469„§cell_idÙ$3ec7c8d3-e5d3-4c7a-ba3c-e0a267131469¤codeÚ)let val(x) = Measurements.value(x) params(row) = (row["Z_o"], val(row["log(M_o/M_sun)"]), row["gamma"]) MZ = (x, param) -> param[1] + log10(1 - exp(-10^((x - param[2]) * param[3]))) set_theme!(theme_black()) f = Figure() ax = Axis( f[1,1], xlabel=L"\log(\mathrm{M_\star / M_\odot})", ylabel=L"12 + \log(\mathrm{O / H})", title=L"\mathrm{Z0 \,\, and \,\, \gamma \,\, fixed}", titlesize=30, xlabelsize=28, ylabelsize=28, xticklabelsize=20, yticklabelsize=20, ) colors = distinguishable_colors( size(df_Z0_gamma_fixed, 1), [RGB(1,1,1), RGB(0,0,0)], dropseed=true, ) for (row, color) in zip(eachrow(df_Z0_gamma_fixed), colors) lines!( ax, 9..11, m -> MZ(m, params(row)); color, label=row["Sample"], ) end axislegend(ax, position=:rb, labelsize=25) f end¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$072bddde-dece-4d9f-990b-e374038ba7e6„§cell_idÙ$072bddde-dece-4d9f-990b-e374038ba7e6¤code»md"## Raw data for M-Z fit"¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$8bd4f390-591f-11ec-0b66-6585ca602deb„§cell_idÙ$8bd4f390-591f-11ec-0b66-6585ca602deb¤codeÙPusing DelimitedFiles, CairoMakie, LaTeXStrings, DataFrames, Measurements, Colors¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$bc031ef8-6fa2-4feb-a354-000960395686„§cell_idÙ$bc031ef8-6fa2-4feb-a354-000960395686¤codeÚ3md""" # Fits ## M-Z relation: ``12 + \log(O / H) = Z_0 + \log\!\left[1 - \exp\!\left(-\left[\dfrac{M_\star}{M_0}\right]^{\!\gamma}\right)\right]`` In this model, ``Z_0`` is the saturation metallicity. It quantifies the asymptotic upper metallicity limit. ``M_0`` is the characteristic turnover mass above which the metallicity asymptotically approaches the upper metallicity limit, ``Z_0``. At stellar masses ``< M_0``, the M-Z relation reduces to a power law with an index ``\gamma``. ## M-redshift relation: ``\log(M_0 / M_⊙) = a + b \, \log(1 + z)`` """¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$34ce6570-6566-4981-908a-81eabcbca7bf„§cell_idÙ$34ce6570-6566-4981-908a-81eabcbca7bf¤codeÚ7begin raw_data_full_fit = readdlm("./data/clean_table_02_full_fit.txt") raw_data_Z0_gamma_fixed = readdlm("./data/clean_table_02_Z0_gamma_fixed.txt") df_full_fit = identity.(DataFrame( raw_data_full_fit[2:end, [1,2,6]], raw_data_full_fit[1, [1,2,6]], )) df_full_fit[!, raw_data_full_fit[1, 3]] = parse_error.( string.(raw_data_full_fit[2:end, 3]) ) df_full_fit[!, raw_data_full_fit[1, 4]] = parse_error.( string.(raw_data_full_fit[2:end, 4]) ) df_full_fit[!, raw_data_full_fit[1, 5]] = parse_error.( string.(raw_data_full_fit[2:end, 5]) ) df_Z0_gamma_fixed = identity.(DataFrame( raw_data_Z0_gamma_fixed[2:end, [1,2,3,5,6]], raw_data_Z0_gamma_fixed[1, [1,2,3,5,6]], )) df_Z0_gamma_fixed[!, raw_data_Z0_gamma_fixed[1, 4]] = parse_error.( string.(raw_data_Z0_gamma_fixed[2:end, 4]) ) end;¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$6b70529a-5941-4c64-92ee-2add064119a4„§cell_idÙ$6b70529a-5941-4c64-92ee-2add064119a4¤codeÙÉmd""" # [Zahid et al. (2014)](https://doi.org/10.1088/0004-637x/791/2/130) ### [Data](https://iopscience.iop.org/0004-637X/791/2/130/suppdata/apj498704t2_ascii.txt?doi=10.1088/0004-637X/791/2/130) """¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$118c5e5e-9845-44f2-b37b-45b39898198a„§cell_idÙ$118c5e5e-9845-44f2-b37b-45b39898198a¤codeÚlet val(x) = Measurements.value(x) params(row) = (val(row["Z_o"]), val(row["log(M_o/M_sun)"]), val(row["gamma"])) MZ = (x, param) -> param[1] + log10(1 - exp(-10^((x - param[2]) * param[3]))) set_theme!(theme_black()) f = Figure() ax = Axis( f[1,1], xlabel=L"\log(\mathrm{M_\star / M_\odot})", ylabel=L"12 + \log(\mathrm{O / H})", title=L"\mathrm{Full \,\, fit}", titlesize=30, xlabelsize=28, ylabelsize=28, xticklabelsize=20, yticklabelsize=20, ) colors = distinguishable_colors( size(df_full_fit, 1), [RGB(1,1,1), RGB(0,0,0)], dropseed=true, ) for (row, color) in zip(eachrow(df_full_fit), colors) lines!( ax, 9..11, m -> MZ(m, params(row)); color, label=row["Sample"], ) end axislegend(ax, position=:rb, labelsize=25) f end¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$fb901ecb-aed9-4a21-818f-b2be8d76e674„§cell_idÙ$fb901ecb-aed9-4a21-818f-b2be8d76e674¤codeÚÞlet Mz = Measurements.value.(df_Z0_gamma_fixed[!, "log(M_o/M_sun)"]) Mz_error = Measurements.uncertainty.(df_Z0_gamma_fixed[!, "log(M_o/M_sun)"]) z = log10.(1 .+ df_Z0_gamma_fixed[!, "Redshift"]) Mz_fit = z -> Measurements.value(fit[1, "a"]) + Measurements.value(fit[1, "b"]) * z set_theme!(theme_black()) f = Figure() ax = Axis( f[1,1], xlabel=L"\log(1 + z)", ylabel=L"\log(\mathrm{M_0 / M_\odot})", title=L"\mathrm{Mass \,\, vs. \,\, redshift}", titlesize=30, xlabelsize=28, ylabelsize=28, xticklabelsize=20, yticklabelsize=20, ) colors = distinguishable_colors( size(df_Z0_gamma_fixed, 1), [RGB(1,1,1), RGB(0,0,0)], dropseed=true, ) for (i, color) in pairs(colors) scatter!( ax, [z[i],], [Mz[i],], label=df_Z0_gamma_fixed[i, "Sample"]; color, ) errorbars!(ax, [z[i]], [Mz[i]], [Mz_error[i]]; color, whiskerwidth=10) end lines!(ax, z, Mz_fit, color=:white, label="Fit") axislegend(ax, position=:rb, labelsize=25) f end¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$e5710a64-1b6f-46a4-9ee3-ac22529caef2„§cell_idÙ$e5710a64-1b6f-46a4-9ee3-ac22529caef2¤codeÙÈfunction parse_error(s::String)::Measurement{Float64} number = parse(Float64, match(r"^.*(?=(\+or-))", s).match) error = parse(Float64, match(r"(?<=\+or-).*", s).match) return number ± error end;¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$32ffc13b-75dd-4986-beba-8766e7c6719b„§cell_idÙ$32ffc13b-75dd-4986-beba-8766e7c6719b¤codeÙTfit = DataFrame( Relation = "M-redshift", a = 9.138 ± 0.003, b = 2.64 ± 0.05, )¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedënotebook_idÙ$a768f3c2-4b3c-11f1-9696-6532a90a8045«in_temp_dir¨metadata€