3C273

• We initially took images of the quasar to locate it, the transmission grating was then places in front of the CCD to obtain its spectrum.
• As 3c273 is an object with a magnitude of 12.9, many frames were taken to try and increase the signal to noise.
• A total of 30 4x4 binned frames were taken with an exposure of 120s
• This is a single frame of 3c273 and its surrounding stars,
• 3c273_Spec_1_Image.jpg.png:
• This is then a stacked image of 30 frames with 3c273 highlighted:
• Full_Bin2_Image.jpg.png:

• The area highlighted on the plot was sliced from the array, and an area just above was also sliced to be used as the background.
• The plot below shows the initial slice without the zeroth order star, the background slice and the slice with the background subtracted,
• Slices.png:
• The final slice was the projected onto the x axis:

• The first image shows 10 frames stacked:
• 3c273_2.png:
• The second image shows all 30 frames stacked:
• 3c273_1.png:
• This plot then shows 30 of the slices stacked in python,
• PythonStack.png:

• To then calibrate the wavelength, a reference spectrum was used from the star Denebola

• Deneb_Star.png:

• The zeroth order star was then fit with a Gaussian to find the centre.

• This was repeated for the reference stars Denebola and Aldebaran and 3c273, the data was then sliced so that the centre of the star (Gaussian) was at zero, and plotted,

• two_Spectrums_Positions.png:

• To then map the pixel position to the wavelength the reference of a line within Denebola was used,
• The line was used which has a wavelength of 486.1 nm,
• To find the position of the line in Denebola it was fit with a voigtian,
• The line was found to fall at the pixel value of 73, however the pixel value needed to be converted into mm.
• The size of a pixel was 0.009 mm however as we used 4x4 binning this was then 0.036 mm.
• The slit density of the grating was set at 200 however this needs to be checked,
• The grating equation was used to find the distance of the grating from the CCD,
• where k is the order = 1, m is the slit density and is the angle of diffraction.

• The angle was related to the distance of the grating from the CCD by,
• where p is the pixel position and l is the distance of the grating from the CCD.
• from these l = 26.9 mm

• This could then be used to map the wavelength position from the pixel number,

• This then gave a plot of

• two_Spectrums.png:

• the spectral line of 3c273 spectrum were then fit with a Voigtian,

• Hbeta.png:

• Halpha.png:

• Which gave the parameters:

 Parameter Amp 0.924 ± 0.1201 1.065 ± 0.6452 565.89 ± 0.0295 753.456± 1.7232 0.5508 ± 5.4785 0.0219 ± 6.9023 20.3071 ± 4.1472 19.6402 ± 5.9619 0.0372 ± 0.0015 0.0867 ± 0.0031 -0.0003 ± 0.0 0.0001 ± 0.0 b_2 0.0 ± 0.0 -0.0 ± 0.0

• The important parameter was the mean, , which give the wavelength of the line,
• This could then be compared to the emitted wavelength of the line to find the redshift: * The redshift was found using:
• The velocity was found using
• And the distance with

 Parameter Observed 565.89 ± 0.0295 753.456± 1.7232 Emitted 486.1 656.3 z 0.16 0.148 v [ms^-1] 4.80*10^7 4.44*10^7 d [Mpc] 707 654 real z 0.158 0.158 real d 750 750

Vega

• The width of the Gaussian from the fit was plotted against the number of points within the convolution:
• where

• Gaussian:
• Lorentz:
• Circle:
• Background:

• Discrete Convolution:

• sig_vs_its.png:

• Our spectrum was attempted to be normalised to the elodie spectrum by fitting an exponential to the elodie spectrum and setting the background of our data to that,

• The exponential was not a great fit so not sure how else to do this.
-- JosephBayley - 18 Feb 2016

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Topic revision: r2 - 19 Feb 2016 - JosephBayley

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