method

astrophysical spectroscopy

Spectroscopy applied to cosmic objects reveals stellar and galactic properties.
10 related articles · 6 formulas

Description

Astrophysical spectroscopy is the analysis of light emitted, absorbed, or scattered by celestial objects to determine their physical and chemical properties. By spreading starlight into its constituent colors, astronomers can read the fingerprints of elements, measure temperatures, densities, and velocities, and even probe magnetic fields and dark matter distributions. This technique is the foundation of modern astrophysics, transforming distant points of light into rich sources of information about the composition and evolution of stars, galaxies, and the universe itself.

History

The technique was pioneered in the 19th century by Joseph von Fraunhofer, who mapped hundreds of dark lines in the solar spectrum, and later by Gustav Kirchhoff and Robert Bunsen, who established the connection between spectral lines and chemical elements. The first stellar spectra were obtained by Angelo Secchi in the 1860s.

How it works

When light passes through a prism or a diffraction grating, it is split into a spectrum. Dark absorption lines or bright emission lines appear at specific wavelengths, corresponding to electronic transitions in atoms and molecules. The positions of these lines reveal which elements are present, while their shifts (Doppler effect) indicate motion toward or away from us. The widths and intensities of the lines provide information about temperature, pressure, and density. For galaxies, spectroscopy of the integrated light reveals stellar populations, star formation rates, and the presence of active galactic nuclei.

In practice

Astrophysical spectroscopy is used to measure the expansion of the universe (redshift), to discover exoplanets via radial velocity method, and to classify galaxies in large surveys like SDSS.

Fun fact

The element helium was discovered in 1868 as a bright yellow line in the spectrum of the Sun before it was ever found on Earth.

Concept graph →

Formulas

$$ rac{z''}{z} rac{ u^2 - 1/4}{ au^2}$$
Approximates background evolution using Hankel index in cosmology.
What is in the formula
zvariablescale factor or redshift depending on context — scale factor
νvariableHankel index — hankel index
τvariableconformal time — conformal time second
''operatorsecond derivative with respect to the independent variable (here, conformal time) — second derivative
\frac{z''}{z}\approx\frac{ν^2-1/4}{\eta^2} · 2607.00636
$$B(k_1,k_2,k_3) = \frac{6}{5} f_{NL} [P(k_1)P(k_2) + P(k_2)P(k_3) + P(k_3)P(k_1)]$$
Bispectrum measures non-Gaussianity in cosmological perturbations.
What is in the formula
BvariableBispectrum of curvature perturbations — bispectrum
k_1, k_2, k_3variableWavenumbers of three modes — wavenumber reciprocal metre
f_{NL}variableNonlinearity parameter — nonlinearity parameter
PvariablePower spectrum of curvature perturbations — power spectrum
b(k_1,k_2,k_3)=\frac{6}{5}f_{nl}[p(k_1)p(k_2)+{2perm.}] · 2607.06692
$$B(k_1,k_2,k_3) \propto (k_1/k_2)^\Delta \cos(\omega \ln(k_1/k_2))$$
Bispectrum shows oscillations from additional fields.
What is in the formula
Bvariablebispectrum — bispectrum cubic metre
k_1variablefirst wavenumber — wavenumber reciprocal metre
k_2variablesecond wavenumber — wavenumber reciprocal metre
k_3variablethird wavenumber — wavenumber reciprocal metre
\Deltavariablespectral tilt — dimensionless
\omegavariableoscillation frequency in log space — dimensionless
\proptooperatorindicates the left side equals the right side times a constant factor — proportionality
\lnoperatorlogarithm to base e — natural logarithm
\cosoperatortrigonometric cosine — cosine
b(k,k,q)\propto(k/q)^δ\cos(ω\ln(k/q)) · 2607.24939v1
$$j_n(x) = \sqrt{\frac{\pi}{2x}} J_{n+1/2}(x)$$
Spherical Bessel functions describe radial waves in spherical coordinates.
What is in the formula
j_nvariableSpherical Bessel function of order n — spherical bessel function
xvariableRadial argument (often kr) — dimensionless argument
J_{n+1/2}variableOrdinary Bessel function of half-integer order — bessel function
j_{-1}(x)=\frac{\cosx}{x} · 2512.20123
$$n_s = 1 - \frac{2}{N}$$
Spectral index deviation from scale invariance depends on e-folds.
What is in the formula
n_svariableScalar spectral index — scalar spectral index
NvariableNumber of e-folds of inflation — e folds
n_s=1-\frac{2}{n_*} · 2605.00735v1
$$ds^2 = -e^{2\rho} dt^2 + e^{2\lambda} dr^2 + r^2 d\Omega^2$$
Metric for spherically symmetric spacetime in general coordinates.
What is in the formula
ds^2variablespacetime interval — spacetime interval metre squared
dtvariablecoordinate time differential — time differential second
drvariableradial coordinate differential — radial coordinate differential metre
dΩ^2variablesolid angle element squared — solid angle element squared
ρvariablemetric function of r and t — metric function
λvariablemetric function of r and t — metric function
rvariableradial coordinate — radial coordinate metre
ds^2=-e^{2ρ}dudv+r^2dω^2 · 2605.00780v1
ds^2=-a(r)dt^2+b(r)^{-1}dr^2+r^2(dθ^2+\sin^2θdφ^2) · 2605.09521v1

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