IOAA 2024, Анализ на данни — Задача 1. D1. Photometric comparison of surveys

(a)

DES is Table 1 and SDSS Table 2, since faint stars will have higher uncertainties. SDSS uses a smaller telescope (2.5 m) than DES (4 m), hence, it is typically shallower and has larger errors. Just looking at the error distribution should be enough to tell who has larger errors.

(b)

The linear regression of each curve:

The reported parameters are:

SDSS:

$A=0.2780$ (acceptable from 0.2502 to 0.3058 which is within 10% range of the fit)

$B=-7.3108$ (acceptable from -8.0419 to -6.5797 which is within 10% range of the fit)

DES:

$A=0.4063$ (acceptable from 0.3657 to 0.4470 which is within 10% range of the fit)

$B=-10.7597$ (acceptable from -10.2217 to -11.2977 which is within 10% range of the fit)

(c)

Using that $S/N\sim1/\operatorname{err}m_g$ and above fits we can arrive at the following:

SDSS: $\log_{10}(\operatorname{err}m_g)=0.2780\cdot21.5-7.3108\ \longrightarrow\ \operatorname{err}m_g=0.0464$

DES: $\log_{10}(\operatorname{err}m_g)=0.4063\cdot21.5-10.7597\ \longrightarrow\ \operatorname{err}m_g=0.0095$

Accepted answers follow below.

(d)

One tip for this question is that the student should realize that the SDSS RA coordinate is sorted, so it can be used as a reference for the scanning of DES coordinates to perform the match. These are the stars that can be matched between catalogs:

(e)

The figure of g magnitude of DES vs SDSS should look like this with the best linear fit:

The student should identify the stars that are closest to the one-to-one line ($x=y$) between surveys. This could be with a zero offset, or a non-zero offset. The two stars that would be suitable for photometric calibration with zero offset are the ones with ID's 8 and 9 of Table 1 (DES). The four stars that would be suitable for photometric calibration with non-zero offset are the ones with ID's 2, 3, 4 and 6 of Table 1 (DES).

Marking scheme — General Rules

These are general guidelines for the grading of all problems. All of the rules listed below refer to deductions on specific items in the marking scheme.

Marking scheme

(a) 5 points

• 5 points: Realize that the data from the left table is from DES, whereas the one from the right table is from SDSS.

(b) 35 points

• 12.5 points: Correct graph for SDSS data using semi-log paper. $\frac{12.5}{14}$ points will be awarded for each correctly placed point.
• 12.5 points: Correct graph for DES data using semi-log paper. $\frac{12.5}{12}$ points will be awarded for each correctly placed point.
• 5 points: Correct parameters A and B for SDSS data. 2.5 points will be awarded for each correct parameter within a 10% range of the correct fit.
• 5 points: Correct parameters A and B for DES data. 2.5 points will be awarded for each correct parameter within a 10% range of the correct fit.

Note: If the student uses a graphical method to obtain parameters A and B but does not draw support lines, then no marks are given. As graphical methods can depart from analytical.

(c) 5 points

• 2.5 points: Obtain correct values for the Signal to Noise ratio ($S/N$) within a 10% range for SDSS.
• 2.5 points: Obtain correct values for the Signal to Noise ratio ($S/N$) within a 10% range for DES.

(d) 15 points

• 15 points: Match correctly the IDs of the data sets. $\frac{15}{7}$ points for each match.

(e) 15 points

• 12 points: Correct graph using millimeter paper. $\frac{12}{7}$ points will be awarded for each correctly placed point and double error bars.
• 3 points: Correct identification of the stars that would be suitable for photometric calibration between the two surveys using ID's of Table 1 (DES).