# The Hubble Constant - History During the 1920s, there was a great debate regarding the presence of other galaxies. By then, telescopes had become powerful enough to pick apart "nebulae", the general term for a gaseous astronomical object used then. One of these cosmologists was Edwin Hubble, who in 1923 used cepheid variables to gauge the distance of the Andromeda Galaxy from us, showing that it was too far away to be in our galaxy. If you're curious on how this was done, Cepheid variables are actually **standard candles**, meaning that provided the periods of brightness fluctuations are equal the luminosity will be the same. This allows you to use it's apparent magnitude to calculate its brightness. In 1929, Hubble was able to plot a graph of all the local galaxies with their relative velocities against their distance. ![[Pasted image 20230706100612.png]] This graph shows that there is a linear regression line which allows us to plot the expansion of the universe. This is Hubble's law, given by: $v = H_{0}d$ **Where**: - $H_0$ is hubble's constant - $d$ is the distance away from the galaxy - $v$ is the velocity of the galaxy relative to us What really stands out to me about this equation is the unit - it's given in kilometres per second per megaParsec - shown below: $\frac{km / s}{mpc}$ At first, Edwin hubble measured the age of the universe as 2 billion years. The age of the Earth is 4.5 billion years! **Standard candles**: an object that always has the same luminosity. At first, Edwin hubble measured the age of the universe as 2 billion years. The age of the Earth is 4.5 billion years! # A Dive into Standard Candles - Measuring Our Universe ## Standard Rulers and Candles - geometric effect - know absolute size of ruler, measure **angular size** of what you see - get distance from 1/r - e.g parallax --> standard candles: - know intrinsic brightness of source - observe apparent brightness - light falls off as a known function of distance --> get distance from difference in the brightnesses / periods - e.g cepheids, bright "marker" galaxies # Finding Distances to a Galaxy We all know (or should know) that Cepheid variables are used as standard candles to discovery of cepheids (variable stars)--> henrietta leavitt observed the cepheid period-luminosity relationship 2nd method--> using brightest stars in a galaxy brightest stars = constant magnitude --> brightest 25 stars assumed to have a constant magntiude in clusters, similar to TRGB method hubble applied this to galaxies with bright O stars --> 3rd method --> constant galaxy luminosity assume total luminosity of any given galaxy is a constant number to determine distances to galaxy clusters # More on using Cepheids Cepheids are **variable stars** - meaning that their brightness changes. For this specific class of star, this change is regular, they have a period-luminosity relationship. They get brighter and then dim in regular intervals. You can plot this graph against the luminosity of the Cepheid and the period of the brightness oscillation. THE LONGER THE PERIOD OF THE CEPHEID, THE HIGHER ITS LUMINOSITY. THIS DOES NOT MEAN ITS APPARENT BRIGHTNESS IS HIGHER. ![[Pasted image 20230706110538.png]] we can use this to get a measure of the distance/total luminosity, plugging in with the apparent magnitude yields us the distances from a galaxy (Check [["Brightness" - Luminosity and Magnitude]]) ![[Pasted image 20230706103850.png]] The period-luminosity relationship of different Cepheid Variables plotted ## The Issues with Cepheids - A Poor Marker? // how confusing two different types of cepheids led to dramatic underestimations in the distances between galaxies --> there are two types of cepheids - type 1 and W virginis variables (W virginis are much less massive + bright) --> used too many W Virginis variables for PL calibration applied this calibration to Classical Cepheids, which are a magnitude and a half brighter - making galaxies too bright --> Baade (famous german astronomer of the early 1900s) thought he could find RR Lyrae stars in Andromeda --> couldn't find, 1.5mags too faint --> only saw brightest stars, TRGB Thackeray, his contemporary --> found the difference between Cepheids and RR Lyrae in LMC and SMC has a difference of 1.5 magnitudes ### The Issue of Interstellar Dust --> many of hubble's brightest "stars" in Virgo were actually HII (star forming) regions, rendering them much brighter than they were and his value for the hubble constant useless --> although many differences in hubble const. calculations difference began to shrink over time --> hubble constant final value --> 72 +- 7 km/s/Mpc --> hubble tension: the perceived difference between calculated values of the hubble constant, leading to different estimates on the age of the universe add diagram from lecnotes about cepheids (with error bars) here! --> notice how there is less spread as the magnitude increases. the luminosity goes up and down --> the temperature has a much larger effect on the magnitude. there is a mean line in the middle of the max/min --> interstellar extinction will allow for infrared to exit meaning there may be more scattering/uncertainty ### Intrinsic Issues with Cepheid Measurements //why cepheid measurements are hard to make --> there are a limited number of **phase points** to measure variability - phase points are a physical time which we measure in days coupled with a magnitude. this means that we can model the period of the cepheid with these. --> we need to constantly measure the magnitudes to be able to create plots of the cepheids' period-temperature relationship/. --> cepheids are also young, massive stars that are in galaxy disks - hence interstellar extinction is really really prevalent, as the interstellar medium contains loads of gas, other stars - meaning there might be interference/abberation/lensing effects that could influence our result. we might be getting light from 10-20 stars in one pixel! --> cepheids are difficult to understand - although we understand how and wy they pulse, we don't understand the effects of metallicity on the pulsations & why they're on the instability strip for example F115W > F160W? (focal length? ) //cepheid distance ladder systematics (issues) --> interstellar extinction --> light blending from foreground stars --> artificial star modelling --> metallicity --> variations in period-luminosity relation --> sample selection --> reddening --> instrument systematics to name a few! all of these errors have to have an error margin of <1%! the cepheids and the supernovae give us a value for the hubble constant at: 73.04 +- 1.04 km/s/Mpc (1.4% precision measurement) # What's Next? For more on Cepheids, go here: [[Cepheid Variables & Other Variable Stars (Astro)]]