## 2.1 Magnitudes Each number of magnitude corresponds to an increase or decrease of *2.5* times. ### *Formulas*: - Relation *[[../Glossary/Absolute Magnitude]] (M) and apparent (m) magnitude* : #### M = m - 5 $log_{10}$ (d/pc)+5 - A - Relation of *apparent magnitude and flux* of two stars: #### m$_2$ - m$_1$ = 2.5$log_{10}$ ($F_1$/$F_2$) {heads up: there is an inverse relationship!} - Relation of *absolute magnitudes and luminosity* of two stars: #### M$_2$ - M$_1$ = 2.5$log_{10}$ ($L_1$/$L_2$) {heads up: there is an inverse relationship!} ## 2.2 Colours of stars and galaxies ### Filters used in photometry: - *U filter* , passes near UV - *B filter*, passes blue - *V filter*, passes green-yellow - *R filter*, passes red light - *I filter*, passes near IR The [[../Glossary/astronomical colour]] of a star is the difference between two apparent magnitudes , eg $m_b$ - $m_r$ . #### A larger value of *(B-R)* indicates a redder star { A larger value of indicates that the B magnitude is numerically larger (i.e. fainter) than the R magnitude. So, such a star must emit relatively more of its light in the red part of its spectrum than in the blue part.} The interstellar medium gives rise to [[../Glossary/extinction (A)]] The amount of extinction is larger is larger in the blue part of the spectrum (U and B) than in the red part (R to K) This known as interstellar [[../Glossary/reddening]] ![[../Assets/Screenshot 2023-10-11 at 20.30.14.png|300]] ## 2.3 Flux and luminosity *[[../Glossary/luminosity]]* is a measure of how much energy in the form of light (or other electromagnetic radiation) is _emitted_ by a star or galaxy in a given time interval. *[[../Glossary/Flux]]* is measure of how much energy in the form of light (or other electromagnetic radiation) we _observe_ from a star or galaxy in a given time interval. *inverse square law* : #### F = L / 4$\pi$ d$^2$ {where *F* is [[../Glossary/Flux]], *L* is [[../Glossary/luminosity]] and d is distance} ## 2.4 Light curves The SNR of a light curve can be improved by [[../Glossary/folding]] multiple light curves Multi-wavelength light curves of galaxies can give an upper limit for the size of the object. This is because information cannot propagate faster than the speed of light. So if (as here) the X-ray emission doubles in brightness in a few hours, the size of the X-ray emitting region cannot be larger than the distance travelled by electromagnetic radiation in that time interval. This interval is known as the [[../Glossary/light travel time]]. ## references: [[Docent/S284 Astronomy]] [[../Assets/TMA1 questions.pdf]] [[Part 1 Astrometry measuring distances]] [[../Glossary/V Band]]