HR-ezddlmZddlZddlmZddlmZmZmZm Z m Z ddl m Z ddl mZmZmZddlZddlmZmZddlmZddlmZddlmZmZdd lmZm Z m!Z!dd l"m#Z#m$Z$dd l%m&Z&dd l'm(Z(dd l)m*Z*ddgZ+ddgiZ,erddl-m.Z.e&rddl/m0Z0ndZ0ej1ej2ej3zz 4dej2z Z5ej24ej6Z7dde zej8zz j9j:Z;dej<z4ej=Z>dej<z4ej?Z@dejAzejBdzz j9j:ZCejD4ejEejFz ZGeddZHeddZIGddeZJGddeZKdS)) annotationsN)abstractmethod)expfloorlogpisqrt)Number) TYPE_CHECKINGAnyTypeVar)infsin) CosmologyFlatCosmologyMixin) Parameter_validate_non_negative_validate_with_unit)aszarrvectorize_redshift_method) HAS_SCIPY) lazyproperty)AstropyUserWarningFLRW FlatFLRWMixin*scipy)Mapping)quadc td)Nz!No module named 'scipy.integrate')ModuleNotFoundError)argskwargss ;lib/python3.11/site-packages/astropy/cosmology/flrw/base.pyrr(s!"EFFF?_FLRWT)bound_FlatFLRWMixinTceZdZdZedddZeddZed d Zed d dZed dZ edde j Z edZ de jzdde jzdfdddfd Ze jdZ e jdZ edZedZedZedZedZedZed Zed!Zed"Zed#Zed$Zed%Zed&Z d'Z!d(Z"d)Z#d*Z$d+Z%d,Z&d-Z'd.Z(d/Z)d0Z*d1Z+d2Z,d3Z-d4Z.d5Z/d6Z0d7Z1d8Z2d9Z3d:Z4d;Z5d<Z6d=Z7e8d>Z9d?Z:d@Z;dAZdDZ?dEZ@e8dFGdHZAdIZBdJZCdKZDdLZEdMZFdNZGe8dOZHdPZIdQZJdRZKdSZLdTZMdUZNdVZOxZPS)Wra A class describing an isotropic and homogeneous (Friedmann-Lemaitre-Robertson-Walker) cosmology. This is an abstract base class -- you cannot instantiate examples of this class, but must work with one of its subclasses, such as :class:`~astropy.cosmology.LambdaCDM` or :class:`~astropy.cosmology.wCDM`. Parameters ---------- H0 : float or scalar quantity-like ['frequency'] Hubble constant at z = 0. If a float, must be in [km/sec/Mpc]. Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Note that this does not include massive neutrinos. Ode0 : float Omega dark energy: density of dark energy in units of the critical density at z=0. Tcmb0 : float or scalar quantity-like ['temperature'], optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : quantity-like ['energy', 'mass'] or array-like, optional Mass of each neutrino species in [eV] (mass-energy equivalency enabled). If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str or None (optional, keyword-only) Name for this cosmological object. meta : mapping or None (optional, keyword-only) Metadata for the cosmology, e.g., a reference. Notes ----- Class instances are immutable -- you cannot change the parameters' values. That is, all of the above attributes (except meta) are read only. For details on how to create performant custom subclasses, see the documentation on :ref:`astropy-cosmology-fast-integrals`. z7Hubble constant as an `~astropy.units.Quantity` at z=0.z km/(s Mpc)scalar)docunit fvalidatez5Omega matter; matter density/critical density at z=0.z non-negative)r0r2z?Omega dark energy; dark energy density/critical density at z=0.floatz;Temperature of the CMB as `~astropy.units.Quantity` at z=0.Kelvinz%Number of effective neutrino species.zMass of neutrino species.eV)r0r1 equivalenciesz>Omega baryon; baryonic matter density/critical density at z=0.)r0gRQ@Nnamemetact|| ||_||_||_||_||_||_||_|dn|j |j z |_ |j j dz |_tj|j z t$j|_|j j t*z} t,| z t$jz|_t2| dzz} | t$jt$jdzz z|_t:|jj dzz|jj z |_d|jz|_ |j!+d|_"d|_#d|_$d|_%dx|_&|_'ntQ|j)|_"|j)|j"z |_#tUj+|j!j dkd} | j,dk|_$t[| |_&|j$r|j!| j nd|_%|j"|j&z |_'|j$rd|j%t\|j zz } | j |_/|j/0|_1|j|2dz|_3n%d |j)z|jz|_3dx|_/|_1d |j z |j4z |jz |j3z |_5|j6|_7d |_8dS) Nr8gY@r'r*grv}+?rFC?r&)9super__init__H0Om0Ode0Tcmb0Neffm_nuOb0_Om0_Ob0_Odm0_H0value_hconstctouMpc_hubble_distance_H0units_to_invs _sec_to_GyrGyr _hubble_time_critdens_constgcm_critical_density0_a_B_c2_Tcmb0_Ogamma0_Tnu0_m_nu _nneutrinos _neff_per_nu _massivenu_massivenu_mass _nmassivenu _nmasslessnur_Neffnpnonzerosizelen_kB_evK_nu_ytolist _nu_y_listnu_relative_density_Onu0_Ode0_Ok0 inv_efunc_inv_efunc_scalar_inv_efunc_scalar_args)selfrArBrCrDrErFrGr9r:H0_scd0valuemassivenu_y __class__s r$r@z FLRW.__init__s d...    ![TTty49/D (.5(!&48!3 7 7 > >x~ 00(4/AE9#T1W,"*acAD!Gm"; $+"3Q"669P9VV ($+5  :  D  $D #DO#'D 37 7D t00$TZ00D !% T-= =D  j!1A!566q9G%lQ.DO"7||D -1_F 7#))$  !% 043C CD  ? 0'7TZ+?@DDJ"j//11DO)A)A!)D)DDDJJ '3dmCDJ+/ /DJ$)Odj04=@4:M "&&(###r%cd||St|||}||jkrtd|S)zCValidate baryon density to None or positive float > matter density.Nz=baryonic density can not be larger than total matter density.)rrB ValueError)rwparamrLs r$rGzFLRW.Ob0sH =L&tUE:: 48  O  r%crt|jx}dks|jjdkrdSt |||}|jd|ffvr#t d|dt|dtj |jdkrt d|j rtj |||}|S) zValidate neutrino masses to right value, units, and shape. There are no neutrinos if floor(Neff) or Tcmb0 are 0. The number of neutrinos must match floor(Neff). Neutrino masses cannot be negative. rNr>u2unexpected number of neutrino masses — expected z, got .z-invalid (negative) neutrino mass encountered.)shape) rrgr]rLrrr~rkrhanyisscalar full_like)rwrrL nneutrinoss r$rFz FLRW.m_nus  ++ +J 1 1T[5F!5K5K4$D%77 ;rJ=1 1 1<&<<.1%jj<<< VEK!O $ $ NLMM M > ALZ@@@E r%cHt|jdko |jdkS)z-Return bool; `True` if the cosmology is flat.r7r&)boolrsOtot0rws r$is_flatz FLRW.is_flat5s%TY#%>DJ#,=???r%cP|j|jz|jz|jz|jzS)7Omega total; the total density/critical density at z=0.)rHr^rqrrrsrs r$rz FLRW.Otot0:s(y4=(4:5 BTYNNr%c|jS)z?Omega dark matter; dark matter density/critical density at z=0.)rJrs r$Odm0z FLRW.Odm0? zr%c|jS)zIOmega curvature; the effective curvature density/critical density at z=0.)rsrs r$Ok0zFLRW.Ok0Ds yr%c|jS)z] Temperature of the neutrino background as `~astropy.units.Quantity` at z=0. )r_rs r$Tnu0z FLRW.Tnu0Is zr%c4|jjdkrdS|jS)z?Does this cosmology have at least one massive neutrino species?rF)r_rLrcrs r$has_massive_nuzFLRW.has_massive_nuPs! : q 5r%c|jS)z:Dimensionless Hubble constant: h = H_0 / 100 [km/sec/Mpc].)rMrs r$hzFLRW.hWs wr%c|jS)z)Hubble time as `~astropy.units.Quantity`.)rWrs r$ hubble_timezFLRW.hubble_time\s   r%c|jS)z-Hubble distance as `~astropy.units.Quantity`.)rSrs r$hubble_distancezFLRW.hubble_distanceas $$r%c|jS)z5Critical density as `~astropy.units.Quantity` at z=0.)r[rs r$critical_density0zFLRW.critical_density0fs &&r%c|jS)z)DNN1,=,=,BBBr%c|jtdt|}|j|dzdzz||dzzS)a Return the density parameter for baryonic matter at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Ob : ndarray or float The density of baryonic matter relative to the critical density at each redshift. Returns `float` if the input is scalar. Raises ------ ValueError If ``Ob0`` is `None`. Nz)Baryon density not set for this cosmologyr&r'r<)rIr~rrtrs r$ObzFLRW.ObsQ( 9 HII I 1IIyAG>)DNN1,=,=,BBBr%c|jtdt|}|j|dzdzz||dzzS)aReturn the density parameter for dark matter at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Odm : ndarray or float The density of non-relativistic dark matter relative to the critical density at each redshift. Returns `float` if the input is scalar. Raises ------ ValueError If ``Ob0`` is `None`. Notes ----- This does not include neutrinos, even if non-relativistic at the redshift of interest. NzSBaryonic density not set for this cosmology, unclear meaning of dark matter densityr&r'r<)rJr~rrtrs r$OdmzFLRW.Odms[2 : 9  1IIzQWN*T^^A->->!-CCCr%ct|}|jdkr+t|drtj|jndS|j|dzdzz||dzzS)a Return the equivalent density parameter for curvature at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Ok : ndarray or float The equivalent density parameter for curvature at each redshift. Returns `float` if the input is scalar. rrr7r&r<)rrshasattrrhzerosrrtrs r$rzFLRW.Oksk 1II 9>>(/7(;(;D28AG$$$ DyAG>)DNN1,=,=,BBBr%ct|}|jdkr+t|drtj|jndS|j||z||dzzS)aReturn the density parameter for dark energy at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Ode : ndarray or float The density of non-relativistic matter relative to the critical density at each redshift. Returns `float` if the input is scalar. rrr7r<)rrrrrhrrde_density_scalertrs r$rzFLRW.Odesq 1II :??(/7(;(;D28AG$$$ DzD11!444t~~a7H7HA7MMMr%crt|}|j|dzdzz||dzzS)aReturn the density parameter for photons at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Ogamma : ndarray or float The energy density of photons relative to the critical density at each redshift. Returns `float` if the input is scalar. r&r*r<)rr^rtrs r$rz FLRW.Ogammas: 1II}CA~-q0A0AQ0FFFr%ct|}|jdkr+t|drtj|jndS||||zS)aReturn the density parameter for neutrinos at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Onu : ndarray or float The energy density of neutrinos relative to the critical density at each redshift. Note that this includes their kinetic energy (if they have mass), so it is not equal to the commonly used :math:`\sum \frac{m_{\nu}}{94 eV}`, which does not include kinetic energy. Returns `float` if the input is scalar. rrr7)rrqrrhrrrrprs r$rzFLRW.Onu.sc$ 1II :??(/7(;(;D28AG$$$ D{{1~~ 8 8 ; ;;;r%c6|jt|dzzS)aIReturn the CMB temperature at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Tcmb : `~astropy.units.Quantity` ['temperature'] The temperature of the CMB in K. r&)r]rrs r$Tcmbz FLRW.TcmbEs{fQii#o..r%c6|jt|dzzS)adReturn the neutrino temperature at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- Tnu : `~astropy.units.Quantity` ['temperature'] The temperature of the cosmic neutrino background in K. r&)r_rrs r$TnuzFLRW.TnuTszVAYY_--r%c\d}t|}|js6||jzt|drt j|jndzSd}d}d}|jdt j|dzz }d||z|zz|z}| d|j z}||j z|zS) aNeutrino density function relative to the energy density in photons. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- f : ndarray or float The neutrino density scaling factor relative to the density in photons at each redshift. Only returns `float` if z is scalar. Notes ----- The density in neutrinos is given by .. math:: \rho_{\nu} \left(a\right) = 0.2271 \, N_{eff} \, f\left(m_{\nu} a / T_{\nu 0} \right) \, \rho_{\gamma} \left( a \right) where .. math:: f \left(y\right) = \frac{120}{7 \pi^4} \int_0^{\infty} \, dx \frac{x^2 \sqrt{x^2 + y^2}} {e^x + 1} assuming that all neutrino species have the same mass. If they have different masses, a similar term is calculated for each one. Note that ``f`` has the asymptotic behavior :math:`f(0) = 1`. This method returns :math:`0.2271 f` using an analytical fitting formula given in Komatsu et al. 2011, ApJS 192, 18. r=rr&gHzG?g'|?gTN?)axis) rrcrgrrhonesrrm expand_dimssumrfrb) rwrprefacpinvpk curr_nu_y rel_mass_perrel_masss r$rpzFLRW.nu_relative_densitycs^ 1II #71g;N;N'Wrwqw'7'7'7TWX   J#qr(B(B(B"BC q9}22t; ##B''$*;;))H44r%cRd|t|dz zS)aInternal convenience function for w(z) integral (eq. 5 of [1]_). Parameters ---------- ln1pz : `~numbers.Number` or scalar ndarray Assumes scalar input, since this should only be called inside an integral. References ---------- .. [1] Linder, E. (2003). Exploring the Expansion History of the Universe. Phys. Rev. Lett., 90, 091301. r&)rr)rwln1pzs r$ _w_integrandzFLRW._w_integrands&TVVCJJ,----r%cNt|}t|ttjfs7tjfd|D}tjd|zStjdt|dzd}t d|zS)a{Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- I : ndarray or float The scaling of the energy density of dark energy with redshift. Returns `float` if the input is scalar. Notes ----- The scaling factor, I, is defined by :math:`\rho(z) = \rho_0 I`, and is given by .. math:: I = \exp \left( 3 \int_{a}^1 \frac{ da^{\prime} }{ a^{\prime} } \left[ 1 + w\left( a^{\prime} \right) \right] \right) The actual integral used is rewritten from [1]_ to be in terms of z. It will generally helpful for subclasses to overload this method if the integral can be done analytically for the particular dark energy equation of state that they implement. References ---------- .. [1] Linder, E. (2003). Exploring the Expansion History of the Universe. Phys. Rev. Lett., 90, 091301. c hg|].}tjdtd|zd/S)rr))rrr).0redshiftrws r$ z)FLRW.de_density_scale..s9TTThd'CH ,=,=>>qATTTr%r'rr&) r isinstancer rhgenericarrayrrrr)rwrivals` r$rzFLRW.de_density_scalesR 1II!fbj122 !8TTTTRSTTTD6!d(## #)1c!c'll;;A>Dq4x== r%c(|j|js|jn|j||zz}t |dz}t j|dz||z|jz|z|jzz|j | |zzS)a\Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- E : ndarray or float The redshift scaling of the Hubble constant. Returns `float` if the input is scalar. Defined such that :math:`H(z) = H_0 E(z)`. Notes ----- It is not necessary to override this method, but if de_density_scale takes a particularly simple form, it may be advantageous to. r&r<) r^rcrqrprrhr rHrsrrrrwrOrzp1s r$efuncz FLRW.efuncs(]? =DJJ!9!9!! ?j400333 4   r%c |j|js|jn|j||zz}t |dz}|dz||z|jz|z|jzz|j||zzdzS)a]Inverse of ``efunc``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- E : ndarray or float The redshift scaling of the inverse Hubble constant. Returns `float` if the input is scalar. r&r<g) r^rcrqrprrHrsrrrrs r$rtzFLRW.inv_efunc s]? =DJJ!9!9!! ?j400333 4 r%c4|j|g|jR|dzz S)aIntegrand of the lookback time (equation 30 of [1]_). Parameters ---------- z : float Input redshift. Returns ------- I : float The integrand for the lookback time. References ---------- .. [1] Hogg, D. (1999). Distance measures in cosmology, section 11. arXiv e-prints, astro-ph/9905116. r&)rurvrs r$_lookback_time_integrand_scalarz$FLRW._lookback_time_integrand_scalar%s+$&t%aF$*EFFF!c'RRr%cVt|}|||dzz S)aIntegrand of the lookback time (equation 30 of [1]_). Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- I : float or array The integrand for the lookback time. References ---------- .. [1] Hogg, D. (1999). Distance measures in cosmology, section 11. arXiv e-prints, astro-ph/9905116. r&rrtrs r$lookback_time_integrandzFLRW.lookback_time_integrand9s*$ 1II~~a  AG,,r%c>|j}|dzdz|j|g|RzS)aIntegrand of the absorption distance [1]_. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- X : float The integrand for the absorption distance. References ---------- .. [1] Hogg, D. (1999). Distance measures in cosmology, section 11. arXiv e-prints, astro-ph/9905116. r&r<)rvru)rwrr"s r$_abs_distance_integrand_scalarz#FLRW._abs_distance_integrand_scalarNs5$*CA~ 6 6q @4 @ @ @@@r%c\t|}|dzdz||zS)aIntegrand of the absorption distance [1]_. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- X : float or array The integrand for the absorption distance. References ---------- .. [1] Hogg, D. (1999). Distance measures in cosmology, section 11. arXiv e-prints, astro-ph/9905116. r&r<rrs r$abs_distance_integrandzFLRW.abs_distance_integrandcs.$ 1IICA~q 1 111r%c<|j||zS)aMHubble parameter (km/s/Mpc) at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- H : `~astropy.units.Quantity` ['frequency'] Hubble parameter at each input redshift. )rKrrs r$HzFLRW.Hxsx$**Q--''r%c,dt|dzz S)aScale factor at redshift ``z``. The scale factor is defined as :math:`a = 1 / (1 + z)`. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- a : ndarray or float Scale factor at each input redshift. Returns `float` if the input is scalar. r&)rrs r$ scale_factorzFLRW.scale_factors fQii#o&&r%c,||S)a)Lookback time in Gyr to redshift ``z``. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] Lookback time in Gyr to each input redshift. See Also -------- z_at_value : Find the redshift corresponding to a lookback time. )_lookback_timers r$ lookback_timezFLRW.lookback_times(""1%%%r%c<|j||zS)aLookback time in Gyr to redshift ``z``. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] Lookback time in Gyr to each input redshift. )rW_integral_lookback_timers r$rzFLRW._lookback_times  4#?#?#B#BBBr%c:t|jd|dS)aLookback time to redshift ``z``. Value in units of Hubble time. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : float or ndarray Lookback time to each input redshift in Hubble time units. Returns `float` if input scalar, `~numpy.ndarray` otherwise. r)rrrs r$rzFLRW._integral_lookback_times$D8!Q??BBr%c||tjztjS)a The lookback distance is the light travel time distance to a given redshift. It is simply c * lookback_time. It may be used to calculate the proper distance between two redshifts, e.g. for the mean free path to ionizing radiation. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- d : `~astropy.units.Quantity` ['length'] Lookback distance in Mpc )rrNrOrPrQrRrs r$lookback_distancezFLRW.lookback_distances/"""1%%/33AE:::r%c,||S)aAge of the universe in Gyr at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] The age of the universe in Gyr at each input redshift. See Also -------- z_at_value : Find the redshift corresponding to an age. )_agers r$agezFLRW.ages"yy||r%c<|j||zS)aAge of the universe in Gyr at redshift ``z``. This internal function exists to be re-defined for optimizations. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] The age of the universe in Gyr at each input redshift. )rW _integral_agers r$rz FLRW._ages  4#5#5a#8#888r%cDt|j|tdS)aEAge of the universe at redshift ``z``. Value in units of Hubble time. Calculated using explicit integration. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : float or ndarray The age of the universe at each input redshift in Hubble time units. Returns `float` if input scalar, `~numpy.ndarray` otherwise. See Also -------- z_at_value : Find the redshift corresponding to an age. r)rrrrs r$rzFLRW._integral_age s*D8!SAA!DDr%cB|j||dzzS)aVCritical density in grams per cubic cm at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- rho : `~astropy.units.Quantity` Critical density in g/cm^3 at each input redshift. r<)r[rrs r$critical_densityzFLRW.critical_density#s!&$**Q--A)===r%c.|d|S)aComoving line-of-sight distance in Mpc at a given redshift. The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving distance in Mpc to each input redshift. r)_comoving_distance_z1z2rs r$comoving_distancezFLRW.comoving_distance2s ++Aq111r%c.|||S)a$ Comoving line-of-sight distance in Mpc between objects at redshifts ``z1`` and ``z2``. The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. Parameters ---------- z1, z2 : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshifts. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving distance in Mpc between each input redshift. ) _integral_comoving_distance_z1z2rwz1z2s r$rzFLRW._comoving_distance_z1z2Ds$44R<<|j|||zS)a Comoving line-of-sight distance in Mpc between objects at redshifts ``z1`` and ``z2``. The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. Parameters ---------- z1, z2 : Quantity-like ['redshift'] or array-like Input redshifts. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving distance in Mpc between each input redshift. )rSrrs r$rz%FLRW._integral_comoving_distance_z1z2ns$"$t'S'STVXZ'['[[[r%c.|d|S)aComoving transverse distance in Mpc at a given redshift. This value is the transverse comoving distance at redshift ``z`` corresponding to an angular separation of 1 radian. This is the same as the comoving distance if :math:`\Omega_k` is zero (as in the current concordance Lambda-CDM model). Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving transverse distance in Mpc at each input redshift. Notes ----- This quantity is also called the 'proper motion distance' in some texts. r)"_comoving_transverse_distance_z1z2rs r$comoving_transverse_distancez!FLRW.comoving_transverse_distances,66q!<<>"s(KKr%c:t|jd|dS)a6Absorption distance at redshift ``z``. This is used to calculate the number of objects with some cross section of absorption and number density intersecting a sightline per unit redshift path ([1]_, [2]_). Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- d : float or ndarray Absorption distance (dimensionless) at each input redshift. Returns `float` if input scalar, `~numpy.ndarray` otherwise. References ---------- .. [1] Hogg, D. (1999). Distance measures in cosmology, section 11. arXiv e-prints, astro-ph/9905116. .. [2] Bahcall, John N. and Peebles, P.J.E. 1969, ApJ, 156L, 7B r)rrrs r$absorption_distancezFLRW.absorption_distance s2D7A>>qAAr%cdtjt||jzdz}t j|t jS)aFDistance modulus at redshift ``z``. The distance modulus is defined as the (apparent magnitude - absolute magnitude) for an object at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- distmod : `~astropy.units.Quantity` ['length'] Distance modulus at each input redshift, in magnitudes. See Also -------- z_at_value : Find the redshift corresponding to a distance modulus. g@g9@)rhlog10r rrLrQQuantitymag)rwrvals r$distmodz FLRW.distmod'sJ0BHS!9!9!!D$:$:1$=$=$BB B  " (  . .q 1 1 7b2q5 C#I.9R"'!cR"WN&:":;;;SXX#b( 77EC$s3xx..$82:e;L;L$LLM MEC$s3xx..$829U;K;K$KKL Lr%c||}|j|dzz||tjzz S)aDifferential comoving volume at redshift z. Useful for calculating the effective comoving volume. For example, allows for integration over a comoving volume that has a sensitivity function that changes with redshift. The total comoving volume is given by integrating ``differential_comoving_volume`` to redshift ``z`` and multiplying by a solid angle. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- dV : `~astropy.units.Quantity` Differential comoving volume per redshift per steradian at each input redshift. r")r rSrrQ steradian)rwrr%s r$differential_comoving_volumez!FLRW.differential_comoving_volumebs?( . .q 1 1$C0DJJqMMQ[4PQQr%cv||tjtz S)a Separation in transverse comoving kpc corresponding to an arcminute at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- d : `~astropy.units.Quantity` ['length'] The distance in comoving kpc corresponding to an arcmin at each input redshift. )r rPrQkpc_radian_in_arcminrs r$kpc_comoving_per_arcminzFLRW.kpc_comoving_per_arcminys. 003366qu==@QQQr%cv||tjtz S)a Separation in transverse proper kpc corresponding to an arcminute at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- d : `~astropy.units.Quantity` ['length'] The distance in proper kpc corresponding to an arcmin at each input redshift. )rrPrQr.r/rs r$kpc_proper_per_arcminzFLRW.kpc_proper_per_arcmins. --a0033AE::=NNNr%cvt||tjz S)a Angular separation in arcsec corresponding to a comoving kpc at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- theta : `~astropy.units.Quantity` ['angle'] The angular separation in arcsec corresponding to a comoving kpc at each input redshift. )_radian_in_arcsecr rPrQr.rs r$arcsec_per_kpc_comovingzFLRW.arcsec_per_kpc_comovings- !4#D#DQ#G#G#J#J15#Q#QQQr%cvt||tjz S)a Angular separation in arcsec corresponding to a proper kpc at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- theta : `~astropy.units.Quantity` ['angle'] The angular separation in arcsec corresponding to a proper kpc at each input redshift. )r4rrPrQr.rs r$arcsec_per_kpc_properzFLRW.arcsec_per_kpc_propers- !4#A#A!#D#D#G#G#N#NNNr%)Q__name__ __module__ __qualname____doc__rrArBrCrDrErQ mass_energyrFrGKr5r@ validatorpropertyrrrrrrrrrrrrrrrrrrrrrrrrrprrrrtrrrrrrrrrrrrrrrrrrrr rrrrrr r)r,r0r2r5r7 __classcell__r|s@r$rrEsF99v  E    B ) C    C 9 M   D I I    E 9 3~   D 9 'd-!-//   D ) L   CACi  14Z e) e)e)e)e)e)e)e)T ]  ]  ^^@@@X@OOXOXXX X X!!X!%%X%''X'XX ==^=2TTT CCC2CCC2DDDBCCC(NNN(GGG$<<<. / / / . . .B5B5B5H... 1!1!1!f   @6SSS(---*AAA*222* ( ( ('''$&&&,CCC$CCC&;;;&&999"EEE, > > >222$===(1%%%YY&%Y*\\\&===0EEEB@@@4@@@6LLL:BBB4&&&6MMM@RRR.RRR$OOO$RRR$OOOOOOOr%ceZdZdZejdZfdZfdZe dd Z d d d dfdZe dZ dZ xZS)ra Mixin class for flat FLRW cosmologies. Do NOT instantiate directly. Must precede the base class in the multiple-inheritance so that this mixin's ``__init__`` proceeds the base class'. Note that all instances of ``FlatFLRWMixin`` are flat, but not all flat cosmologies are instances of ``FlatFLRWMixin``. As example, ``LambdaCDM`` **may** be flat (for the a specific set of parameter values), but ``FlatLambdaCDM`` **will** be flat. T)derivedctd|jjvrt ddS)NrCz>subclasses of `FlatFLRWMixin` cannot have `Ode0` in `__init__`)r?__init_subclass___init_signature parameters TypeError)clsr|s r$rEzFlatFLRWMixin.__init_subclass__sG !!### S(3 3 3P  4 3r%ctj|i|d|_d|j|jz|jz|jzz |_dS)Nr7r&)r?r@rsrHr^rqrr)rwr"kwr|s r$r@zFlatFLRWMixin.__init__sM$%"%%% DI 5 BTYNO r%rwr-returnr+c |jjjdi|jd|ji}|j|ji|j}|jdzD]$}t|d|zt||%|S)NrC)r_r>) __nonflatclass__rF bind_partial_init_argumentsrCr"r#__all_parameters__setattrgetattr)rwbainstns r$nonflatzFlatFLRWMixin.nonflats@T " 2 ?  "  )-   %t$bg;;;(83 5 5A D#'74#3#3 4 4 4 4 r%Nr: to_nonflatr:Mapping | NonerZrr#r c <tjd||d|S)a8Returns a copy of this object with updated parameters, as specified. This cannot be used to change the type of the cosmology, except for changing to the non-flat version of this cosmology. Parameters ---------- meta : mapping or None (optional, keyword-only) Metadata that will update the current metadata. to_nonflat : bool or None, optional keyword-only Whether to change to the non-flat version of this cosmology. **kwargs Cosmology parameter (and name) modifications. If any parameter is changed and a new name is not given, the name will be set to "[old name] (modified)". Returns ------- newcosmo : `~astropy.cosmology.Cosmology` subclass instance A new instance of this class with updated parameters as specified. If no arguments are given, then a reference to this object is returned instead of copy. Examples -------- To make a copy of the ``Planck13`` cosmology with a different matter density (``Om0``), and a new name: >>> from astropy.cosmology import Planck13 >>> Planck13.clone(name="Modified Planck 2013", Om0=0.35) FlatLambdaCDM(name="Modified Planck 2013", H0=67.77 km / (Mpc s), Om0=0.35, ... If no name is specified, the new name will note the modification. >>> Planck13.clone(Om0=0.35).name 'Planck13 (modified)' The keyword 'to_nonflat' can be used to clone on the non-flat equivalent cosmology. >>> Planck13.clone(to_nonflat=True) LambdaCDM(name="Planck13", ... >>> Planck13.clone(H0=70, to_nonflat=True) LambdaCDM(name="Planck13 (modified)", H0=70.0 km / (Mpc s), ... With 'to_nonflat' `True`, ``Ode0`` can be modified. >>> Planck13.clone(to_nonflat=True, Ode0=1) LambdaCDM(name="Planck13 (modified)", H0=67.77 km / (Mpc s), Om0=0.30712, Ode0=1.0, ... rYr>)r?clone)rwr:rZr#r|s r$r]zFlatFLRWMixin.clones)puww}H$:HHHHHr%cdS)rr&r>rs r$rzFlatFLRWMixin.Otot0%s sr%ctt|ttjfrdntj|dS)a<The total density parameter at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshifts. Returns ------- Otot : ndarray or float Returns float if input scalar. Value of 1. r&F)subok)rr rhr ones_likers r$rzFlatFLRWMixin.Otot*s6a&"*!566 XCCBLRWr%r$rs@#"""""**************..........!!!!!!@@@@@@@@ FEEEEEEE888888111111777777 ? #gY'('''''' G$$$$$$$GGGDAC!%K(,,S13Y77cffQUmm B().4YNN18,,YNN18,, u~  * / 5 ),,qtacz " "  ( ( ('+?CCC zOzOzOzOzO9zOzOzOz+w w w w w &w w w w w r%