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where are we going today I thought we would talk about ngc2 which is this guy just here the little one you may remember a little while ago we talked about NGC one just in passing I mentioned that ngc2 is actually although it looks like it's sort of a companion is nothing at all to do with NGC one and it's actually much further away what's this paper looking at on screen here's another picture of ngc1 and ngc2 which doesn't look quite as nice as the one that I was showing you before that's because I took it from my back Garden tell me how you took it what's the process long exposure or how does it work I think this was about probably about an hour so it's only a little four and a half inch telescope quite a small
telescope so you have to kind of point it at anything for quite a while to see much you'd be pretty proud of your pictures aren't you I'm just amazed you can see anything at all for my pack Garden to be honest your intuition might tell you that it's further away because it's smaller but of course not all galaxies are the same size so it could actually be a small Galaxy that's much closer to us or it could be you know a little bit smaller than ngz1 and at the same distance so we need some other way of figuring out what the distances the galaxies are there are two ways you can kind of figure out the distances to things one is that we can just use the expansion of the universe because the
universe is expanding when a galaxy is further away as the light comes towards us the universe is expanding which stretches out its light which means that when it arrives at us the wavelength has been stretched to a longer wavelength so this is this phenomenon called redshift the further a galaxy is away from us the more the universe has expanded in the time it's taken the light to get from where it started out to where we are and therefore the more redshifted it is and so that's this thing called the Hubble law that says that the further a galaxy is away from you the bigger the red shift you'll measure for it so we've got the spectrum of the Galaxy it's got lots of these little absorption lines due to
the various chemical elements that make up its stars as a Galaxy's redshifted those little lines are all just shifted in way wavelength towards the red end of the spectrum so you just measure how much they've been shifted you can think of it as a velocity if you like it's how fast the Galaxy is moving but it also very directly tells you how far away it is sounds like problem solved it does and in fact so here's the numbers for this galaxy we can have a look so what we got we've got ngc2 is here and here's the measurement of its redshift turned into a velocity and it's like a bit over seven and a half thousand kilometers per second it's how big it's redshift is you can turn it into a distance and so actually if you
turn it into a distance you get a number you get the number down here which is 114 million past X away and the relationship between those two numbers the velocity and the distance is this thing called the Hubble law and the constant between them is this thing called Hubble's Constant and actually you have to worry a little bit about other things for example the earth going around the Sun's going around the Galaxy's moving relative to space or the cosmic microwave background or whatever you want to measure it relative to so those all add velocities as well and so actually the numbers below are just various attempts to kind of correct for those effects but they don't actually change things very much you know you turn from 7500 to what
seven thousand two hundred makes a little bit of a difference but not a huge difference so that was ngc2 remember that seven and a half thousand kilometers per second let's go back to the bigger Galaxy NGC one and you do the same measurement you get four and a half thousand kilometers per second so smaller velocity means smaller distance so as your intuition probably told you that means that this galaxy is about 50 closer than this galaxy oh loads closer quite a lot closer yeah so that's one way of measuring the distances but you have to worry a little bit about you know maybe there are other velocities going on maybe there are other things that might be messing this up and actually you also have to calibrate that
relationship in that I sort of very glibly told you how you go from velocity to a distance which means you need that constant in between the Hubble constant and we need some way of actually calibrating what that Hubble constant actually is which means we need other ways of measuring distances to things there is a nice way of trying to measure the distances to these galaxies that's independent of the Hubble law and everything else that's independent of everything so it's a kind of a direct measurement of their distance and that's the thing called the Tully Fisher relation named after the two astronomers Tully and Fisher who first came up with this idea in the 1970s I guess and the
idea is okay you need some way of measuring some property of this galaxy that's kind of independent of its distance and comparing it to kind of The observed property so the thing you might want to know is how intrinsically bright is this galaxy because if you knew how intrinsically bright it is then from how bright it appears to be that will tell you how far away it is but the problem is different galaxies have different intrinsic brightnesses so that's no good galaxies are not on their own these things called standard candles they're not all the same brightness so you can't just say oh that one appears much fainter than that one so it's much further away but there is this indirect
technique of saying okay so we can't measure the intrinsic brightness of the thing but one thing we can measure is how fast the Galaxy is rotating and again that actually just depends on the doctor shift again we measure the shifts in spectral lines and you can see so if you've got a nice incline Galaxy which is rotating one side of it's going to be coming towards us the other side is going to be going away from us so we can measure the Doppler shifts within the Galaxy and that tells us how fast it's rotating and of course that doesn't depend on distance right if I took the same galaxy and moved it twice as far away and made the same measurement I'd still measure the same speed of rotation
I think it would be a slightly harder measurement to make because it would be fainter but you'd still get the same answer and the reason why that's interesting is because effectively what that rate of rotation is telling you is what the mass of the Galaxy is in that if you have a more massive Galaxy it rotates faster and so if you make a sort of a slight leap that says that the mass of a galaxy is in some way related to how luminous it is how intrinsically bright it is then that gives you a sort of distance independent way of measuring the intrinsic brightness of a galaxy you measure how fast it's rotating that tells you how much mass there is you then say okay so for that much mass I expect this much luminosity in terms of
stars and so therefore that's the intrinsic Luminosity of the Galaxy and this really only works for spiral galaxies they have sort of similar efficiencies of star formation and they form their Stars at the same time and so on if you make that measurement for spiral galaxies you find that rotation speed which you usually get from the radio part of the spectrum so measuring 21 centimeter line to see how much broaden the lines are which is telling you how fast the Galaxy is rotating and you have to correct it for things for example if the Galaxy's face on then actually you won't see any motion towards you away from you because all the Motions in the plane of the sky so you have to correct for its inclination and various things like that
when you go through all that process you find that there is actually quite a tight relationship which means you really can go from how fast the Galaxy is rotating to its intrinsic Luminosity with a reasonable error that's a little bit of uncertainty because there's some scatter in that relation so then you know it's intrinsic luminosity then go look at how bright it appears to be and putting those two things together then tells you its distance so here's our two galaxies again let's start with ngc2 there's a bunch of measurements it's redshift we already talked about but then there are these redshift independent distances and so the number one I was actually looking at was this figure from 2013 which is a
relatively recent television measurement of the distance of this Galaxy and it comes out at 88 megaparse x so 88 Million past X away if we look at NGC one the other Galaxy the one that we from the Hubble relationship we said was near more nearby the same tally Fisher measurement so there's one stun in 2013 give an answer of 74 Mega parsecs 74 million parsecs away we still have the answer that ngc2 is further away than ngc1 but actually it's not much right by this direct measurement 74 versus what do we have 88 it's about 20 whereas if we you just use the Hubble law we ended up with an answer which is about 50 60 further away you know if you try and do this telephision method you really
shouldn't believe any individual measurement that much because scatter in the relationship and so actually the Luminosity you've kind of inferred for the Galaxy is not that well tied down so there's probably a fair amount of uncertainty which then translates into a fair amount of uncertainty in its distance and so what would be a way of dealing with that well supposing you made a measurement of a whole bunch of galaxies then all those kind of random effects would all average out and so anything that's left over really would be a real difference in the distances between the method you get from the expansion of the universe and the method you get from these sort of direct measures of distances to things
let me refer to a paper here we go this is actually that 2013 paper that we were looking at before where those measurements came from and you can see actually that Tully and Fisher The Originators this method are authors on this paper so they're still very interested in the technique but they've effectively measured for many thousands of galaxies the distances both from the expansion of the universe and from these more direct measured methods of actually measuring a distance and if you make if you subtract one from the other that kind of tells you what the difference between them is and so if you do that for a whole bunch of galaxies on the sky and again this is Tully's work so the red ones are probably ones where
the distance you get from the Hubble law is further away than the distance you get from these direct methods and blue ones it's the other way around and so if it was all just down to the fact that well you know this uncertainty in any individual measurement then there'd be no patterns in this picture it would just be kind of random scattering of red and blue dots but it clearly isn't a random scattering of red and blue dots there's lots and lots of red over here and lots of blue over there for example and this is a manifestation of a phenomenon to do with the fact that the expansion of the universe isn't the only thing that contributes to the speed of the galaxies and they have these things
called peculiar velocities which is just like each Galaxy as well as kind of respecting the overall expansion of the universe is doing its own thing so it might be orbiting a companion it might be Falling Towards a cluster so it has its own velocity and there's no way of separating out well what's the velocity due to the expansion of the universe and what's the expansion due to these other things that are going on except by doing this kind of thing and so what they're actually seeing here this huge effect over an enormous region of space is a gravitational effect due to a thing called the greater tractor and the greater tractor is this Mass out there in space if you think about what happens
everything's expanding but the things on the near side of it are feeling the gravitational pull of that greater tractor and so they're Falling Towards it so as well as the expansion of the universe they're traveling a bit faster because they're being tugged towards it things on the far side are also expanding with the universe but they're being pulled back a bit by the greater tractor like it's a handbrake it's slowing them down right so it's kind of dragging trying to drag them back trying to hold that expansion and so this sort of systematic pattern where you see extra velocity in some places and less velocity in other places is a manifestation a way of seeing that there
are these huge concentrations of mass in the universe which are kind of messing up that overall expansion of the universe by adding in extra fairly large-scale motions of galaxies so what's the final decision how do you finally decide how far away a galaxy is you can't trust any individual measurement like from the television relation that much because there's just uncertain certainty due to the relation and its calibration and all those kinds of things okay so you can't trust that just the Hubble expansion of the universe because they're all these large-scale flows and things going on once you've mapped out what those large-scale flows are you can actually correct for them in your measurements of the velocities of the
galaxies and once you've corrected for them then potentially all that you're seeing then is the smooth expansion of the universe and then you can use the Hubble law having corrected for all these other effects to try and get a distance to it personally I think probably it's a bit of a mugs game I don't think anyone's ever going to really believe the absolute distance to any single Galaxy because they're always going to be uncertainties associated with it but fortunately if you're looking for these kind of large-scale effects all those uncertainties in any individual Galaxy kind of average out and you really can get a good picture of what's going on overall in the universe zodiac signs because why would you want
13 zodiac signs and not a nice round 12 right rather than 13. so if you were born between the 29th of November and the 18th of December technically the sun was in officus and not Sagittarius
