WARP – Week 3

Captain’s log, stardate: -303877.

The Theoreticians

Riker’s hard work was finally paying off as Picard and Data now had the tools to combat their daunting task: overcoming the error hordes by fighting fire with fire. It had worked countless times over millennia of conflict – Picard could not help but reflect on the poetic futility of endless interstellar war.

We started off by finishing calculating errors that were started last week for the Coding Wizards to use to generate clouds of theoretical stars. This was done by creating a subset of the average errors in the x-axis and y-axis of their graph and finding their average value using a function within TOPCAT. Histograms of these errors were created to show where the peak errors were within the data, an example of which is shown below.

A histogram of the errors in the y-axis of the Coding Wizards’ graph for all of the data points given.

Riker had had enough. He hoped to immobilise the error threat by removing the most threatening within their ranks, in effect, cutting the head from this most dangerous of snakes.  

As we needed to narrow down our data, we had to filter out extreme values and pick a reasonable limit to the error in both axes using the histograms. We started with a maximum error of 0.5 in the y-axis and 0.15 on the x-axis but when we plotted this data on top of the coding team’s produced data, we had too many potential extremely metal-poor stars (stars beneath the coloured cloud).

An initial plot of bodies overlaying the theoretical clouds produced by the coding team.

Some errors had slipped past our brave away team. They were dealt with swiftly and efficiently, but with a sense of restraint and control only seen among the most composed Starfleet officers.

After placing error bars on this graph, we realised we had used the unfiltered data which still contained errors outside of our range, as well as points with no errors, so we plotted the correct data of stars with errors within our error range. We believed there were still too many stars within the potential extremely metal-poor area, so we further reduced the error limits to 0.2 for the y-axis and 0.1 for the x-axis, making sure to only use the reduced catalogue rather than the whole data set. The average errors in the axes were again given to the coding team and we plotted our newly reduced data against the coding team’s newly altered data to give the figure below.

A plot of stars (reduced using their errors) overlaying the theoretical clouds produced by the coding team.

This graph shows that there are a lot less potential extremely metal-poor stars, but the coding team needs to increase the x-axis range of the cloud so that the data can be cut more accurately.

The Coding Wizards

Picard and Data prepared themselves for a confrontation with their own creations, thousands of points generated by the very thing they hoped to destroy: The Errors.

This week we aimed to firstly produce code that would, according to a Gaussian distribution, generate a random spread of points for each theoretical data point, using the error (σ) that was determined from the actual data. This theoretical ‘cloud’ of stars would then be available to be overlaid over our actual measurements, thus allowing cuts and reduction of the data to only the most metal-poor stars that were in similar locations to the theoretical metal-poor star ‘clouds’.

Picard never did like seeing merely numbers, in a brief reprieve between combatting the ever-looming error threat, he took a trip to the holodeck where he could gaze to his heart’s content upon a beautiful star of his own creation.  

While waiting for the error in the actual data to be provided, we produced a plot of the NB392 filter and g filter over the spectrum of a F-type star.

The spectrum of an F-type star overlayed with NB392 and g filters.

As can easily be seen that the Ca II K absorption line is present within the range of the NB392 filter’s range. 

As well, we produced a plot of our theoretical data using the axes we have finally decided upon using: (NB392-u)-(g-i) against g-i. 

The theoretical data plotted as (NB392-u)-(g-i) against g-i.

Upon receiving errors for both axes, σ(NB392-u)-(g-i)=0.16149 and σ(g-i)=0.08831, we were able to produce a plot of the theoretical distribution after each star was modelled as a Gaussian for 4000 data points.

Picard gazed upon the deep red smudges and couldn’t help but think of the blood of his crew which would cover his hands should this mission fail. This thought troubled him greatly. He locked it deep within his labyrinthine mind. Thoughts like that at such a crucial time would only inch him further towards he and his loyal crew’s undoing.

The theoretical clouds of stars produced using the errors given by the Theoreticians.

Later, we were provided with more strictly determined errors, σ(NB392-u)-(g-i)=0.106753 and σ(g-i)=0.56765, which allowed us to produce the following distribution plot of our theoretical data. 

The updated theoretical clouds of stars produced using the new errors provided.

As can be seen, the respective metallicity regions are more defined with these new errors. 

We spent a short while determining how to correctly use the “Polyfit” python module, as we were informed this would be a possible method of creating this line by our mentor. 

After this, we decided to attempt different methods to make the cut line, one would be to create a Polyfit line which would fit to the mean points of all the closest points -5.0 and -4.0 metallicity stars.  

The other would be to generate a colour map for the metallicities of the stars. Using our theoretical stars, the metallicities of these stars were assigned to the z-axis, which had a Gaussian fitted to then smooth out the single points. From this, we generated a smooth map of different metallicity points. This plot can be seen below. All future stars can be mapped against this plot and their metallicity calculated from where they lie with respect to the colour map.

A colour map for metallicities generated from theoretical stars. The points are the original stars that were used to calculate the map.

We aim to create this line over the following week in preparation for the next lab session. We will also calculate the error in the metallicity from the error in colour given to us. From this, we should be able to pass the observational data, calculate the metallicities (with errors) and thus make more cuts.

Aside: LCdr. La Forge expressed discontent with Cdr. Riker’s choice of biscuits for the weekly tea break, noting that the orange-flavoured Earth snack, known as “Jaffa Cakes”, were not biscuits but, in fact, cakes. The ship’s stockpile was, nonetheless, completely cleared in a matter of minutes.

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