Dark Matter Evidence: Galactic Rotation Curves

Continuing my discussion of dark matter, I will now explain another piece of evidence supporting its existence: galactic rotation curves.

How rotation curves work is easily understood using basic Newtonian gravitation and assuming spherical symmetry. In a spherically symmetric system (where the properties of the system depend only on the distance from the center (the radius) and not the direction.

Due to the inverse square force law, the force on an object in a spherically symmetric system is equivalent to the force of a point mass at the origin with the total mass at radii less than that of the object. So,

{\bf F}(r) = -\frac{Gm}{r^2}{\bf\hat{r}}\int\limits_0^{r}4\pi s^2 ds \rho(s) = -\frac{GM(r)m}{r^2}{\bf\hat{r}}

where m is the mass of the object, ρ(r) is the mass density at radius r, and M(r) is the mass of the galaxy held within a sphere of radius r. For a circular orbit, this requires that

{\bf F}(r) = -\frac{m v^2}{r}{\bf \hat{r}}

as well. Combining these results, we see that the mass is related to the rotational velocity v by

M(r) = \frac{rv(r)^2}{G}.

We can use measurements of the rotational velocities of objects around the centers of galaxies to estimate the mass and compare these to other methods. In particular, we see that galaxies appear to have a fairly well-defined size. Above some radius there aren’t any more stars. We might then expect the mass to cease increasing, so the velocity will then fall with 1/r.

In the 1970s, Rubin and Ford (and a few other colleagues) made a number of measurements of the velocity curves for a number of spiral galaxies. Some example papers can be found here and here. These galaxies appear to have something more akin to cylindrical symmetry than spherical symmetry, so the above equations won’t be exactly correct, but similar behavior will be expected. The velocity curves were measured by carefully taking spectrographic measurements at different positions in the galaxies. The positions of absorption and emission lines will change slightly depending on the velocities with respect to us, so the positions of these lines allow astronomers to extract the velocities from the data.

Rather than finding this 1/r behavior far from the centers of galaxies, they found that the velocity curves actually leveled off or in some cases increased even far beyond where stars appeared to be. This kind of rotation curve suggests that the total mass is approximately proportional to the radius. Alternatively, this means that the density is proportional to 1/r2.

This gradual reduction in the mass density means that much of the mass of galaxies seems to be spread over a much larger volume than the gas and stars. This mass is not emitting or absorbing light, since otherwise it would be easily detected with photodetectors. A simple explanation of this phenomenon is that the masses of galaxies are dominated by diffuse clouds of nonluminous “dark” matter. This dark matter provides most of the gravitational effects of galaxies except right near the center where normal matter is concentrated.

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Washington Post to Cease Using Redskins Name

Earlier today, the Washington Post announced that it is the latest media outlet to banish the name of the Washington Redskins football team from its pages. This change affects only the editorial page, which has greater control over content than other pages. They also note that their criticism of the name has a more than 20 year history.

This is significant for several reasons: The Post is both a major national newspaper and the premier local newspaper of the DC area. Having an outlet like this join the campaign against the team’s name may have much more of an effect than random online magazines or TV & radio stations in other markets doing the same. It makes the issue much more prominent both on the national stage and in local Washington news.

The NCAA has done an admirable job at pressuring schools to abandon similar mascots. A few schools have (or at least claim to have) the support and consent of local Native American tribes for the use of names and symbols. Otherwise, team names like the “Indians” (Stanford and Dartmouth being two prominent examples: now the Cardinal and the Big Green) have all but disappeared from the college sports landscape. Pro sports haven’t really made any serious attempts at doing the same, so the Cleveland Indians, Atlanta Braves, Chicago Blackhawks, Kansas City Chiefs, and Washington Redskins retain their names. Of these, Washington seems pretty clearly to be the most likely to offend, using a name considered by many to be a racial slur. I suspect that the way the pro leagues working is the reason why they haven’t been able to change as much. Colleges are fully independent teams operating under the auspices of the NCAA. They have the freedom to choose who they will play and can pressure other schools to change by refusing to play them. Pro teams have no such luxury, so the responsibility falls to the league to enact any changes. There appears to be a growing consensus that Washington’s name is an embarrassment to the league, so maybe the name will change if it starts hurting the team’s or the league’s profits.

New Dark Matter Result from PandaX

The PandaX group has released their first dark matter result, which can be found here. PandaX is a dual-phase liquid xenon detector, similar to XENON-100 and LUX. The actual result is not particularly interesting, but PandaX is an interesting experiment because it is one of the first particle physics experiments to be hosted in China. The collaboration is mostly from China but includes a few people from institutions in the US.

Police to Public: You Will Respect My Authoritah!

Another post related to the Ferguson controversy, since it’s still a big news story…

 

According to news reports, it looks like the unrest in Ferguson may finally be waning. News media are also reporting some demographic info on the people who have been arrested. An NPR report suggests that the vast majority of people arrested were not from the town, which really bolsters the case made by a number of people that the violence, looting, and vandalism was driven mainly by outside agitators.

What I really want to talk about is an opinion piece in the Washington Post by an LAPD officer who also teaches at a for-profit college called Colorado Technical University that has angered basically everyone. The criticism is so widespread that the story was featured on CNN.

The author’s basic argument is that people should do whatever police tell them to do and look like they enjoy it if they don’t want to get hurt. In other words, he is the real-life equivalent to Cartman in this episode of South Park. He also basically says that cops are on edge all the time and might hurt people at the slightest provocation. He at least admits that there are bad police officers and that people have rights but does not say how people can invoke their rights without being seen as “challenging” the police, which will of course invite a violent response. He also mentions that people should be empathetic toward officers and provide them with the same amount of respect that officers are supposed to – but often don’t – give the community. This portrayal of police, which is supposed to make us understand their plight, only makes them seem like the worst possible people to entrust with the duty of protecting the public. It’s also important to note that the LAPD, which employs the author, is one of the most notorious departments in the country for its problems with the surrounding community.

The problems with the author’s argument should be quite obvious and tons of people have attacked the piece. The idea that people should be automatically deferential toward police relegates non-police to a second-class status. The suggestion that people not complain or resist illegal police actions because courts can take care of problems gives police carte blanche to violate the Constitution until a more powerful police force comes to stop them. If people can’t directly confront blatantly illegal actions by law enforcement then they have no rights other than those the police allow them to have. If the author wants to position himself as an advocate for more reasonable police-community interactions, this is not the way to do it.

The Discovery Channel Continues Its Long, Sad Decline

In other TV news (though this is about a week old):

In a sign of the continuing decline of educational programming on basic cable, the Discovery Channel created another fake documentary about Megalodon sharks surviving to the present day for this year’s shark week. Megalodons have been extinct for millions of years so this was in no way educational.

It actually wasn’t that long ago when the Discovery Channel was mostly educational programming about science. Channels like Discovery, the History Channel, Animal Planet, and even TLC provided a great deal of educational programming that was also very appealing to children, getting them interested in these sorts of things too. There were always some programs about ridiculous topics like UFOs and conspiracy theories (though good programs on these debunking these and teaching people how to think critically about such topics are certainly possible and probably even useful to make).

It’s unfortunate that these channels – the main educational channels on basic cable – have declined so much. They’ve been mostly indistinguishable from any other channel for a number of years – airing mostly reality shows and cheap documentaries (real or otherwise)/.