# Normalizing the supernova spectrum by photometry

I have a SN spectrum here (already reduced) that seems to have some artifacts. Professor tells me that I may have to normalize it using photometry. As far as I understand, I just have to multiply it by some factor to make the integral over all frequencies equal to bolometric luminosity. Am I right, or is there some more complicated thing here?

## 1 Answer

I think you understood correctly.

Just to be clear. Your photometric data have enough images including bias, flat, and standard stars, and are reduced + calibrated with standard stars. And, your issue is that you can reduce spectrographs (with bias, flat, and arc lamp) but you don't have standard stars for the calibration. Hence, you want to calibrate your spectra with the photometric data. Is this correct?

The following is for more detailed example how to proceed this.

First, note that a photometric data point is the accumulation of photons within a bandpass. See the response curve shown here for example. In the example, B band has its effective wavelength 4353 A, FWHM 781 A, and with its own shape of the response function.

For simplicity, the following demonstration will assume that the response function of the B band is delta function, i.e., zero elsewhere except at 4353 A. We will extend this example to other response function later. Suppose that you have a spectrum containing 4353 A, and you want to calibrate it with the known B photometry. So you can find a ratio = flux(B; photometry) / flux(B; spectrum), and apply this ratio elsewhere in your spectrum.

Note that the spectrum and photometry must be from the same epoch ideally. Otherwise, use the nearest available epoch as an approximation.

If you have more than one photometric data points to calibrate the one spectrum, ideally the ratios elsewhere will be the same. Realistically, they are not. Hence, you average the ratios by somehow.

Next, if you would like to consider the dispersion of the response function, instead of using the flux at a point, you accumulate the fluxes by considering the shape of the response function.

For simplicity, let's say the B band response function is a Heaviside step function = 1 within [4353-781, 4353+781] A and = 0 elsewhere. So, you accumulate the fluxes weighted by the response function from your spectrum. Then find the ratio, and follow the rest of the process.

• Great, thanks! Only, in my case both photometry and spectra are already reduced, however, professor thinks that reducing the spectra is not enough. – Tajimura Nov 14 '18 at 1:41
• what if I only have apparent magnitudes for photometry and no fluxes? – Tajimura Nov 17 '18 at 10:59
• magnitude is the flux. You just have to transform it correctly. – Kornpob Bhirombhakdi Nov 17 '18 at 12:06