## Bandpass Systems Each letter in the following systems designate a section of light of the electromagnetic spectrum. ![[bandpassFilters.png|align:center]] ### UBVRI Filters *(Also known as **Johnson/Bessel system** or **Johnson-Morgan system**) ![[UBVRI.jpg|aling:center|500]] The UBVRI system utilizes a set of defined photometric filters for source classification in the following frequency bands. | Abbrev. | Bandpass | Wavelength Range | Effective Wavelength Midpoint | |:-------:| -------------------- |:-----------------------:|:-----------------------------:| | U | Ultraviolet | $320 - 400 \; {\rm nm}$ | $365 \; {\rm nm}$ | | B | Blue | $400 - 500 \; {\rm nm}$ | $445 \; {\rm nm}$ | | V | Vert(Green) / Visual | $500 - 700 \; {\rm nm}$ | $551 \; {\rm nm}$ | | R | Red | $550 - 800 \; {\rm nm}$ | $658 \; {\rm nm}$ | | I | Infrared | $700 - 900 \; {\rm nm}$ | $806 \; {\rm nm}$ | Each filter has an associated transmission function, $T_{X}(\nu)$, that determines what percent of the [[Flux]] is let through at a given frequency or wavelength. ### Sloan Digital Sky Survey (SDSS) Filters ![[SDSS_filters.jpg|align:center|500]] Similar to the [[#UBVRI Filters]], but more modernized and standardized. ## Spectral Energy Distrbutions Radio - tends to use frequency Optical - tends to use wavelength X-ray / Gamma-Ray - measure in - photon number density ($F = dN/dE$) in units of $\left[ \pu{photons cm^{-2} s^{-1} keV^{-1}} \right]$ - energy flux ($F_{E} = E \frac{\mathrm{d} N}{\mathrm{d} E}$) in units off $\left[ \pu{ erg cm^{-2} s^{-1} keV^{-1}} \right]$ Astronomers tend to plot $\log(\nu)$- $\log(\nu F_{\nu})$ (called a spectral energy distribution in x-ray astronomy, other fields use this term more loosely) - the area under the curve is directly assocaited to the energy within the system - For wavelength: $\log(\lambda)$ - $\log(\lambda F_{\lambda})$ - For energy: $\log(E)$ - $\log(E^{2} \frac{\mathrm{d} N}{\mathrm{d} E})$ With astronomical photometry, we work with integrated flux over some bandpass $ F_{\rm bandpass}^{\rm obs} = \int_{\nu_{1}}^{\nu_{2}} F_{\nu}(\nu) R(\nu) \; \mathrm{d} \nu \hspace{1cm} \text{where} \hspace{1cm} \begin{aligned} F_{\nu}(\nu) &\equiv \text{source spectrum} \\ R(\nu) &\equiv \text{instrument response} = \prod {\rm efficencies} \end{aligned} $