Scientific Analysis of Amateur Spectra

Vocabulary flashcards covering fundamental terms, concepts, and formulas from the lecture on amateur astronomical spectroscopy, flux calibration, and data reduction.

Star Analyser SA100

A low-resolution transmission diffraction grating manufactured by Paton Hawksley with $100\,\text{lines/mm}$, designed to be mounted in a standard $1\frac{1}{4}\text{''}$ filter holder in front of a camera sensor or behind a telescope.

Spectral Resolution ($R$)

A dimensionless quantity describing a spectrograph's ability to resolve fine spectral details, defined as $R = \frac{\lambda}{\Delta\lambda}$, where $\Delta\lambda$ is the Full Width at Half Maximum (FWHM) of a line at wavelength $\lambda$.

Low Resolution Spectroscopy

Spectroscopy performed at $R < 2000$, which allows observing the entire optical spectrum (such as $3800\,\text{\AA}$ to $7400\,\text{\AA}$) simultaneously in one exposure.

High Resolution Spectroscopy

Spectroscopy performed at $R > 10000$, providing detailed line profile information over a narrow wavelength range (e.g., $\sim 100\,\text{\AA}$ wide).

Tilt

A 2D spectral image misalignment where the recorded spectrum is tilted relative to the X-axis of the camera sensor.

Slant

A 2D spectral image distortion where the spectroscope slit orientation is tilted vertically relative to the detector grid.

Smile

An optical distortion within a spectroscope that causes straight spectral lines to become curved across the 2D detector.

Dispersion Equation

A polynomial relationship, typically 3rd or 4th order in detector X-coordinate (e.g., $\lambda = a_0 + a_1 X + a_2 X^2 + a_3 X^3 + a_4 X^4$), used to translate pixel coordinates into calibrated wavelengths in $\text{\AA}$.

Telluric Lines

Atmospheric absorption lines produced by terrestrial gases and water vapor, used as wavelength calibration standards or accuracy checks in high-resolution spectroscopy.

Aerosol Scattering

Atmospheric light extinction caused by dust and water vapor, rising slowly at shorter wavelengths ($\propto \lambda^{-1}$) and forming the main extinction source at wavelengths above $\sim 6000\,\text{\AA}$.

Rayleigh Scattering

Atmospheric light scattering caused by atmospheric gas molecules, increasing rapidly toward shorter wavelengths ($\propto \lambda^{-4}$) and dominating extinction at the blue end of the optical spectrum.

Aerosol Optical Depth (AOD)

A quantitative measurement of atmospheric light attenuation due to atmospheric aerosols and haze, typically ranging from $0.01$ in very dry conditions to $0.4$ in moist environments.

MILES Library

A database of $985$ empirical medium-resolution ($\text{FWHM} \approx 2.5\,\text{\AA}$) stellar spectra corrected for atmospheric and interstellar extinction, widely utilized to select reference stars for instrumental response calibration.

Pickles Library

A spectral flux library consisting of $131$ synthesized average stellar spectra representing various spectral types and luminosity classes free of interstellar extinction.

Rectification

The mathematical processing step of fitting a smooth continuum profile to a spectrum and dividing the spectrum by that continuum to produce a continuum normalized near unity across all wavelengths.

Normalisation

The operation of scaling spectral flux profiles so that the intensity at a chosen reference wavelength (e.g., $6630\,\text{\AA}$) equals unity.

DER_SNR Algorithm

A robust signal-to-noise measurement algorithm defined as $\text{DER\_SNR} = \frac{\text{signal}}{\text{noise}}$ where $\text{signal} = \text{median}(\text{flux}_i)$ and $\text{noise} = \frac{1.482602}{\sqrt{6.0}} \times \text{median}(|2 \text{flux}_i - \text{flux}_{i-2} - \text{flux}_{i+2}|)$.

Equivalent Width (EW)

A measure of spectral line strength representing the integrated area of an absorption or emission line relative to the continuum: $\text{EW} = \sum \left(\frac{F_c - F_\lambda}{F_c}\right) d\lambda$, expressed in $\text{\AA}$ (positive for absorption lines, negative for emission lines).

Spectrophotometry

The science and technique of calibrating astronomical spectra in absolute physical flux units (e.g., $\text{erg\,cm}^{-2}\text{s}^{-1}\text{\AA}^{-1}$).

CALSPEC Archive

A collection of $93$ spectrophotometric standard star spectra observed by the Hubble Space Telescope (HST) with an absolute flux precision better than $2\%$ in the visual spectrum.

Spectroscopic Zero Point ($ZP$)

A calibration constant for a specific photometric filter passband $V(\lambda)$ that relates the bandpass-integrated absolute flux to apparent magnitude via $ZP = -m_S - 2.5 \log_{10}\left(\int V(\lambda) A_S(\lambda)\,d\lambda\right)$.

Interstellar Extinction

The reduction in starlight intensity caused by absorption and scattering by dust grains composed of silicates and carbonaceous materials in the interstellar medium.

Interstellar Reddening

Wavelength-dependent interstellar extinction where shorter (bluer) wavelengths are preferentially scattered, quantified by the color excess $E(B-V) = (B-V) - (B-V)_0$.

Total-to-Selective Extinction Ratio ($R_V$)

The ratio $R_V = \frac{A_V}{E(B-V)}$ relating total V-band extinction $A_V$ to color excess $E(B-V)$, which averages $3.1 \pm 0.1$ in the diffuse galactic interstellar medium.

Cardelli Extinction Law

An empirical formulation of the wavelength dependence of interstellar extinction parameterized as $\frac{A_\lambda}{A_V} = a(x) + \frac{b(x)}{R_V}$, where $x = \frac{1}{\lambda}$ in $\mu\text{m}^{-1}$.

Balmer Decrement

The observed flux ratio of hydrogen Balmer emission lines (such as $H\alpha / H\beta$) used to determine interstellar extinction $E(B-V)$ by comparing measured ratios to theoretical intrinsic values (e.g., $2.86$).