# Measuring Hubble's Constant - Continuing from Before Our first estimate for the Hubble constant came from the measure of radial velocities using the doppler shifts of galaxies - this told us how fast a galaxy was receding from us, allowing us to create an estimate for the doppler shifts of galaxies. This correlation of radial (meaning we took the velocities of the velocities to the distances of the galaxies was first conducted by **Vesto Melvin Slipher** - a prominent astronomer back in the day! Although Hubble's Law takes its' name from the eponymous Hubble Tension, a similar relationship was first measured and described by Georges Lemaître - a priest and physicist in his own right. Therefore, it's been commonly known to others as the *Hubble-Lemaître Law*, though Lemaître was willing to forgo recognition in favour of Hubble. In his 1927 paper, Lemaître had even described an estimate for the Hubble Constant - though that was removed in its english translation. *If you need a break or don't really understand what I'm talking about, check out*[[The Expansion of the Universe (Astro)#The Hubble Constant - History|the original document]] *for more!** --> hubble chart --> creates a line graph with approximate constant of 500 km/s/mpc (actual hubble constant is 70 km/s/mpc) %%find the hubble chart / make your own! make sure you give examples. %% # Finding the Hubble Constant - Methods While Cepheids and Type Ia Supernovae are reliable their use starts to wane after a redshift of z=2 - corresponding to an approximate distance of 10 billion light years. This is when our measurements start to become unreliable - meaning we'll have to revamp them or find other methods to completely ignore this. ## Using the CMB Our first method revolves around using the [[The Cosmic Microwave Background(s) (Astro)|CMB]] to estimate the Hubble constant. It's based on this thing called "**Lambda-CDM cosmology**", a model of what we think makes up the universe and how we think it interacts over cosmic time. This is basically what we've used to predict dark matter - the "lambda" in the model's name is used to associate with dark energy and dark matter, which also has a negative pressure (showing us that dark matter/energy has a negative mass). Look, I'll keep going, but we're going to be touching relativity, so there'll be maths! Short things short - we get a value of $67.66 \pm \ 0.42$ A couple of you might've thought that if we look far enough we could see the plasma from the big bang. Sorry to break it to you, but that's going to be redshifted to oblivion by the time it gets here - it's going to be in the far infrared, way past even the ranges of JWST. However, we can use the knowledge that the Universe was an Opaque plasma to our benefit - //friedman equations: - different constituents of the universe\ %%find and break down? %% CMB + BAO (baryon) measurement --> 67.66 +- 0.42 km/s/Mpc needed to predict the angular scale and physical scale of the sound horizon baryon acoustic oscillations - another way to detect cosmic distances Besides, if all else fails we can also use standard rulers to extrapolate the distances to galaxies. Is there no other [[Cepheid Variables & Other Variable Stars (Astro)|Cepheid]]? //friedman equations: - different constituents of the universe\ %%find and break down? %% CMB + BAO (baryon) measurement --> 67.66 +- 0.42 km/s/Mpc //three-run distance ladder - observationally, the hubble constant describes the relationship between the recessive velocity of galaxies and their distances - we use **Type 1a supernovae** as a candle - always same luminosity, can be used as distance calibrators - supernovae are bright and have equal luminosities - can be seen up to a redshift of z=2 (10b years ago) and are common enough to be useful to use ## Using RR Lyrae Variables - A Third Method //alternative to the distance scale - red giant branch tip stars --> using the stars at the very cusp of the red giant branch as standard candles --> once these stars ignite helium burning, they become brighter. this flash actually happens at the same energy/mass, although these stars are dimmer than cepheids. (core mass, not solar mass!). this is as the star just needs to get to a specific density to fuse benefits of this method --> you only need one epoch of observations, not over a long, long period of time --> they can be pop2 stars, so they can be in the halos of galaxies, which are not as crowded (mitigates extinction/blending) cons --> these stars are not as bright meaning their ranges are limited - RED GIANT CMD FROM SLIDE HERE NOW! - GRAPH OF ALL H_0 VALUES HERE NOW! --> note the relative probability density (for accuracies) - the differences in hubble constant values imply that the errors are caused by systematic errors - hubble constant over time - note the decrease in error bar length! # Hubble Units - Extended! Remember that Hubble's constant is universal and describes the ratio of the rate of change of the universe's expansion against its current expansion: $H_{0} = \frac{\dot{a}}{a}|_{t = 0}$ The units of the Hubble Constant, km/s/mpc, can also be written as 1/s given that km and megaparsecs are both denominations of distance. This allows us to define the **Hubble time** as the inverse of the Hubble constant (giving us a unit of just s), creating the equation: $t_{hub} = \frac{1}{H_{0}}$ This gives us a value for the age of the universe: $t_{hub} = $ hubble radius (R) --> $R = \frac{c}{H_{0}}$ $\frac{\frac{L}{T}}{T^{-1}}$ This gives us a hubble radius, which gives us an estimate for the **observable** universe: $R = 4280mpc$ # Modern Hubble Tension Time to summarise! Since we've got two ways to calculate the Hubble constant, each giving us the mystery of a different value. These two models are the **CMB model** and the **Calibrated Distance** Hubble Tension - which when averaged give us an estimate of 70 km/sMpc (which is very good) but CMB hubble constant value --> 67 - model of empirical data - extermely precise (but accurate!) - standard "ruler" --> measuring angular size, projection Cepheids hubble constant value --> 73 (difference in calculations depending on the candle!) - purely empirical - accuracy and precision ambiguous? - standard candle --> measure magnitudes! since there are two different measurements for the hubble constant, we need to figure out why! this entails us adding new physics to our current cosmological model, which would be very exciting! (error bars on error bars!)