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Luminosity

Protostellar photospheric and accretion luminosities.

LuminosityObject

Zero-age main sequence and accretion luminosities for a protostar.

Implements ZAMS mass-luminosity and mass-radius fits, combined with an accretion model, to compute a protostar's total (photospheric + accretion) luminosity and its FUV-band fraction.

Parameters:

Name Type Description Default
accObj object

Accretion model instance (e.g. PowerLawAccrete) exposing an acc method.

 required

Attributes:

Name Type Description
accObj object

See Parameters.
Source code in src/ocotillopmf/luminosity.py 
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class LuminosityObject:
    """Zero-age main sequence and accretion luminosities for a protostar.

    Implements ZAMS mass-luminosity and mass-radius fits, combined with
    an accretion model, to compute a protostar's total (photospheric +
    accretion) luminosity and its FUV-band fraction.

    Parameters
    ----------
    accObj : object
        Accretion model instance (e.g.
        [`PowerLawAccrete`][ocotillopmf.accretion.PowerLawAccrete]) exposing an
        ``acc`` method.

    Attributes
    ----------
    accObj : object
        See Parameters.
    """

    # PARAMETERS
    RSUN = 6.957e10
    LSUN = 3.848e33
    ALPHA = 0.39704170
    BETA = 8.52762600
    GAMMA = 0.00025546
    DELTA = 5.43288900
    EPSILON = 5.56357900
    ZETA = 0.78866060
    ETA = 0.00586685
    THETA = 1.71535900
    IOTA = 6.59778800
    KAPPA = 10.08855000
    LAMBDA = 1.01249500
    MU = 0.07490166
    NU = 0.01077422
    XI = 3.08223400
    UPSILON = 17.84778000
    PI = 0.00022582
    G = 6.67259e-8
    MSUN = 1.988e33

    accObj: PowerLawAccrete | None = None

    def lZAMS(self, m: ArrayLike) -> float | np.ndarray:
        """Zero-age main sequence luminosity fit.

        Parameters
        ----------
        m : float or array_like
            Stellar mass, in Msun.

        Returns
        -------
        float or ndarray
            ZAMS luminosity, in Lsun.
        """
        LZAMS = (self.ALPHA * m**5.5 + self.BETA * m**11) / (
            self.GAMMA
            + m**3
            + self.DELTA * m**5
            + self.EPSILON * m**7
            + self.ZETA * m**8
            + self.ETA * m**9.5
        )
        return LZAMS

    def rZAMS(self, m: ArrayLike) -> float | np.ndarray:
        """Zero-age main sequence radius fit.

        Parameters
        ----------
        m : float or array_like
            Stellar mass, in Msun.

        Returns
        -------
        float or ndarray
            ZAMS radius, in Rsun.
        """
        RZAMS = (
            self.THETA * m**2.5
            + self.IOTA * m**6.5
            + self.KAPPA * m**11
            + self.LAMBDA * m**19
            + self.MU * m**19.5
        ) / (
            self.NU
            + self.XI * m**2
            + self.UPSILON * m**8.5
            + m**18.5
            + self.PI * m**19.5
        )
        return RZAMS

    def LZAMS(self, m: ArrayLike, mf: ArrayLike) -> float | np.ndarray:
        """Zero-age main sequence luminosity, in cgs units.

        Parameters
        ----------
        m : float or array_like
            Current stellar mass, in Msun.
        mf : float or array_like
            Final stellar mass, in Msun. Unused; kept for a consistent
            ``(m, mf)`` call signature across luminosity methods.

        Returns
        -------
        float or ndarray
            ZAMS luminosity, in erg/s.
        """
        LZ = self.lZAMS(m) * self.LSUN
        return LZ

    def LACC(
        self, m: ArrayLike, mf: ArrayLike, r: ArrayLike
    ) -> float | np.ndarray:  # All in solar units
        """Accretion luminosity.

        Parameters
        ----------
        m : float or array_like
            Current stellar mass, in Msun.
        mf : float or array_like
            Final stellar mass, in Msun.
        r : float or array_like
            Stellar radius, in Rsun.

        Returns
        -------
        float or ndarray
            Accretion luminosity, in erg/s.
        """
        solarAcc_to_cgs = 6.305286e25  # to g/s
        LA = (self.G * (m * self.MSUN) * self.accObj.acc(m, mf) * solarAcc_to_cgs) / (
            r * self.RSUN
        )
        return LA

    def FUV_Frac(self, L: ArrayLike, r: ArrayLike) -> float | np.ndarray:
        """Fraction of luminosity emitted in the FUV band.

        Estimates an effective temperature from `L` and `r`, then looks
        up the corresponding FUV fraction from a tabulated blackbody
        FUV-fraction curve.

        Parameters
        ----------
        L : float or array_like
            Luminosity, in erg/s.
        r : float or array_like
            Radius, in cm.

        Returns
        -------
        float or ndarray
            Fraction of `L` emitted in the FUV band, in [0, 1].
        """
        SIGMA = 5.6704e-5
        Teff = (L / (4.0 * np.pi * r * r * SIGMA)) ** (0.25)
        x_arr = [
            3.0,
            3.11111111111,
            3.22222222222,
            3.33333333333,
            3.44444444444,
            3.55555555556,
            3.66666666667,
            3.77777777778,
            3.88888888889,
            4.0,
            4.07142857143,
            4.14285714286,
            4.21428571429,
            4.28571428571,
            4.35714285714,
            4.42857142857,
            4.5,
            4.57142857143,
            4.64285714286,
            4.71428571429,
            4.78571428571,
            4.85714285714,
            4.92857142857,
            5.0,
            5.11111111111,
            5.22222222222,
            5.33333333333,
            5.44444444444,
            5.55555555556,
            5.66666666667,
            5.77777777778,
            5.88888888889,
            6.0,
        ]
        f_arr = [
            0.0,
            1.36770358435e-16,
            8.61653258138e-15,
            5.26258146666e-11,
            3.70098840631e-08,
            5.0568717347e-06,
            0.000195192270093,
            0.00284793494426,
            0.0197126224006,
            0.0772881806527,
            0.147011634854,
            0.240578127358,
            0.345971543508,
            0.444191207643,
            0.515303033114,
            0.54557500541,
            0.532074541579,
            0.482402999901,
            0.410347804342,
            0.330421281869,
            0.253964856801,
            0.187726633597,
            0.134328849088,
            0.0935685411832,
            0.0510859708182,
            0.0267964291578,
            0.0136432190711,
            0.00679353459533,
            0.00332675938709,
            0.00160869232546,
            0.000770502283946,
            0.000366365690472,
            0.000173237354368,
        ]
        frac = si.interp1d(x_arr, f_arr, kind="linear")
        try:
            ff = []
            for ti in Teff:
                if (np.log10(ti) < 3) or (np.log10(ti) > 6):
                    ff.append(0.0)
                else:
                    ff.append(frac(np.log10(ti)))
            return np.array(ff)
        except TypeError:
            if (np.log10(Teff) < 3) or (np.log10(Teff) > 6):
                return 0.0
            else:
                return frac(np.log10(Teff))

    def FUV_LUM(
        self, m: ArrayLike, mf: ArrayLike, r: ArrayLike
    ) -> float | np.ndarray:
        """Total FUV luminosity, combining ZAMS and accretion components.

        Parameters
        ----------
        m : float or array_like
            Current stellar mass, in Msun.
        mf : float or array_like
            Final stellar mass, in Msun.
        r : float or array_like
            Stellar radius, in Rsun.

        Returns
        -------
        float or ndarray
            Combined ZAMS + accretion FUV luminosity, in erg/s.
        """
        lz = self.LZAMS(m, mf)
        la = self.LACC(m, mf, r)
        lzfuv = lz * self.FUV_Frac(lz, r * self.RSUN)
        lafuv = la * self.FUV_Frac(la, r * self.RSUN)
        return lzfuv + lafuv

    def __init__(self, accObj: PowerLawAccrete) -> None:
        self.accObj = accObj

lZAMS(m)

Zero-age main sequence luminosity fit.

Parameters:

Name Type Description Default
m float or array_like

Stellar mass, in Msun.

 required

Returns:

Type Description
float or ndarray

ZAMS luminosity, in Lsun.
Source code in src/ocotillopmf/luminosity.py 
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def lZAMS(self, m: ArrayLike) -> float | np.ndarray:
    """Zero-age main sequence luminosity fit.

    Parameters
    ----------
    m : float or array_like
        Stellar mass, in Msun.

    Returns
    -------
    float or ndarray
        ZAMS luminosity, in Lsun.
    """
    LZAMS = (self.ALPHA * m**5.5 + self.BETA * m**11) / (
        self.GAMMA
        + m**3
        + self.DELTA * m**5
        + self.EPSILON * m**7
        + self.ZETA * m**8
        + self.ETA * m**9.5
    )
    return LZAMS

rZAMS(m)

Zero-age main sequence radius fit.

Parameters:

Name Type Description Default
m float or array_like

Stellar mass, in Msun.

 required

Returns:

Type Description
float or ndarray

ZAMS radius, in Rsun.
Source code in src/ocotillopmf/luminosity.py 
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def rZAMS(self, m: ArrayLike) -> float | np.ndarray:
    """Zero-age main sequence radius fit.

    Parameters
    ----------
    m : float or array_like
        Stellar mass, in Msun.

    Returns
    -------
    float or ndarray
        ZAMS radius, in Rsun.
    """
    RZAMS = (
        self.THETA * m**2.5
        + self.IOTA * m**6.5
        + self.KAPPA * m**11
        + self.LAMBDA * m**19
        + self.MU * m**19.5
    ) / (
        self.NU
        + self.XI * m**2
        + self.UPSILON * m**8.5
        + m**18.5
        + self.PI * m**19.5
    )
    return RZAMS

LZAMS(m, mf)

Zero-age main sequence luminosity, in cgs units.

Parameters:

Name Type Description Default
m float or array_like

Current stellar mass, in Msun.

 required
mf float or array_like

Final stellar mass, in Msun. Unused; kept for a consistent (m, mf) call signature across luminosity methods.

 required

Returns:

Type Description
float or ndarray

ZAMS luminosity, in erg/s.
Source code in src/ocotillopmf/luminosity.py 
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def LZAMS(self, m: ArrayLike, mf: ArrayLike) -> float | np.ndarray:
    """Zero-age main sequence luminosity, in cgs units.

    Parameters
    ----------
    m : float or array_like
        Current stellar mass, in Msun.
    mf : float or array_like
        Final stellar mass, in Msun. Unused; kept for a consistent
        ``(m, mf)`` call signature across luminosity methods.

    Returns
    -------
    float or ndarray
        ZAMS luminosity, in erg/s.
    """
    LZ = self.lZAMS(m) * self.LSUN
    return LZ

LACC(m, mf, r)

Accretion luminosity.

Parameters:

Name Type Description Default
m float or array_like

Current stellar mass, in Msun.

 required
mf float or array_like

Final stellar mass, in Msun.

 required
r float or array_like

Stellar radius, in Rsun.

 required

Returns:

Type Description
float or ndarray

Accretion luminosity, in erg/s.
Source code in src/ocotillopmf/luminosity.py 
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def LACC(
    self, m: ArrayLike, mf: ArrayLike, r: ArrayLike
) -> float | np.ndarray:  # All in solar units
    """Accretion luminosity.

    Parameters
    ----------
    m : float or array_like
        Current stellar mass, in Msun.
    mf : float or array_like
        Final stellar mass, in Msun.
    r : float or array_like
        Stellar radius, in Rsun.

    Returns
    -------
    float or ndarray
        Accretion luminosity, in erg/s.
    """
    solarAcc_to_cgs = 6.305286e25  # to g/s
    LA = (self.G * (m * self.MSUN) * self.accObj.acc(m, mf) * solarAcc_to_cgs) / (
        r * self.RSUN
    )
    return LA

FUV_Frac(L, r)

Fraction of luminosity emitted in the FUV band.

Estimates an effective temperature from L and r, then looks up the corresponding FUV fraction from a tabulated blackbody FUV-fraction curve.

Parameters:

Name Type Description Default
L float or array_like

Luminosity, in erg/s.

 required
r float or array_like

Radius, in cm.

 required

Returns:

Type Description
float or ndarray

Fraction of L emitted in the FUV band, in [0, 1].
Source code in src/ocotillopmf/luminosity.py 
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def FUV_Frac(self, L: ArrayLike, r: ArrayLike) -> float | np.ndarray:
    """Fraction of luminosity emitted in the FUV band.

    Estimates an effective temperature from `L` and `r`, then looks
    up the corresponding FUV fraction from a tabulated blackbody
    FUV-fraction curve.

    Parameters
    ----------
    L : float or array_like
        Luminosity, in erg/s.
    r : float or array_like
        Radius, in cm.

    Returns
    -------
    float or ndarray
        Fraction of `L` emitted in the FUV band, in [0, 1].
    """
    SIGMA = 5.6704e-5
    Teff = (L / (4.0 * np.pi * r * r * SIGMA)) ** (0.25)
    x_arr = [
        3.0,
        3.11111111111,
        3.22222222222,
        3.33333333333,
        3.44444444444,
        3.55555555556,
        3.66666666667,
        3.77777777778,
        3.88888888889,
        4.0,
        4.07142857143,
        4.14285714286,
        4.21428571429,
        4.28571428571,
        4.35714285714,
        4.42857142857,
        4.5,
        4.57142857143,
        4.64285714286,
        4.71428571429,
        4.78571428571,
        4.85714285714,
        4.92857142857,
        5.0,
        5.11111111111,
        5.22222222222,
        5.33333333333,
        5.44444444444,
        5.55555555556,
        5.66666666667,
        5.77777777778,
        5.88888888889,
        6.0,
    ]
    f_arr = [
        0.0,
        1.36770358435e-16,
        8.61653258138e-15,
        5.26258146666e-11,
        3.70098840631e-08,
        5.0568717347e-06,
        0.000195192270093,
        0.00284793494426,
        0.0197126224006,
        0.0772881806527,
        0.147011634854,
        0.240578127358,
        0.345971543508,
        0.444191207643,
        0.515303033114,
        0.54557500541,
        0.532074541579,
        0.482402999901,
        0.410347804342,
        0.330421281869,
        0.253964856801,
        0.187726633597,
        0.134328849088,
        0.0935685411832,
        0.0510859708182,
        0.0267964291578,
        0.0136432190711,
        0.00679353459533,
        0.00332675938709,
        0.00160869232546,
        0.000770502283946,
        0.000366365690472,
        0.000173237354368,
    ]
    frac = si.interp1d(x_arr, f_arr, kind="linear")
    try:
        ff = []
        for ti in Teff:
            if (np.log10(ti) < 3) or (np.log10(ti) > 6):
                ff.append(0.0)
            else:
                ff.append(frac(np.log10(ti)))
        return np.array(ff)
    except TypeError:
        if (np.log10(Teff) < 3) or (np.log10(Teff) > 6):
            return 0.0
        else:
            return frac(np.log10(Teff))

FUV_LUM(m, mf, r)

Total FUV luminosity, combining ZAMS and accretion components.

Parameters:

Name Type Description Default
m float or array_like

Current stellar mass, in Msun.

 required
mf float or array_like

Final stellar mass, in Msun.

 required
r float or array_like

Stellar radius, in Rsun.

 required

Returns:

Type Description
float or ndarray

Combined ZAMS + accretion FUV luminosity, in erg/s.
Source code in src/ocotillopmf/luminosity.py 
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def FUV_LUM(
    self, m: ArrayLike, mf: ArrayLike, r: ArrayLike
) -> float | np.ndarray:
    """Total FUV luminosity, combining ZAMS and accretion components.

    Parameters
    ----------
    m : float or array_like
        Current stellar mass, in Msun.
    mf : float or array_like
        Final stellar mass, in Msun.
    r : float or array_like
        Stellar radius, in Rsun.

    Returns
    -------
    float or ndarray
        Combined ZAMS + accretion FUV luminosity, in erg/s.
    """
    lz = self.LZAMS(m, mf)
    la = self.LACC(m, mf, r)
    lzfuv = lz * self.FUV_Frac(lz, r * self.RSUN)
    lafuv = la * self.FUV_Frac(la, r * self.RSUN)
    return lzfuv + lafuv