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2.1. Type II Supernovae and the Expanding Photosphere Method

Massive stars come in a wide variety of luminosities and sizes and would seemingly not be useful objects for making distance measurements under the standard candle assumption. However, from a radiative transfer standpoint these objects are relatively simple and can be modeled with sufficient accuracy to measure distances to approximately 10%. The expanding photosphere method (EPM), was developed by Kirshner and Kwan [44], and implemented on a large number of objects by Schmidt et al. [86] after considerable improvement in the theoretical understanding of type II SN (SNII) atmospheres [15, 16, 99].

EPM assumes that SNII radiate as dilute blackbodies

Equation 1 (1)

where thetaph is the angular size of the photosphere of the SN, Rph is the radius of the photosphere, D is the distance to the SN, Flambda is the observed flux density of the SN, and Blambda(T) is the Planck function at a temperature T. Since SNII are not perfect blackbodies, we include a correction factor, zeta, which is calculated from radiate transfer models of SNII. SNe freely expand, and

Equation 2 (2)

where vph is the observed velocity of material at the position of the photosphere, and t is the time elapsed since the time of explosion, t0. For most stars, the stellar radius, R0, at the time of explosion is negligible, and Eqs. (1-2) can be combined to yield

Equation 3 (3)

By observing a SNII at several epochs, measuring the flux density and temperature of the SN (via broad band photometry) and vph from the minima of the weakest lines in the SN spectrum, we can solve simultaneously for the time of explosion and distance to the SNII. The key to successfully measuring distances via EPM is an accurate calculation of zeta(T). Requisite calculations were performed by Eastman et al. [16] but, unfortunately, no other calculations of zeta(T) have yet been published for typical SNIIP progenitors.

Hamuy et al. [34] and Leonard et al. [52] have measured the distances to SN1999em, and they have investigated other aspects of EPM. Hamuy et al. [34] challenged the prescription of measuring velocities from the minima of weak lines and developed a framework of cross correlating spectra with synthesized spectra to estimate the velocity of material at the photosphere. This different prescription does lead to small systematic differences in estimated velocity using weak lines but, provided the modeled spectra are good representations of real objects, this method should be more correct. At present, a revision of the EPM distance scale using this method of estimating vph has not been made.

Leonard et al. [51] have obtained spectropolarimetry of SN1999em at many epochs and see polarization intrinsic to the SN which is consistent with the SN have asymmetries of 10 - 20%. Asymmetries at this level are found in most SNII [101], and may ultimately limit the accuracy EPM can achieve on a single object (sigma ~ 10%). However, the mean of all SNII distances should remain unbiased.

Type II SNe have played an important role in measuring the Hubble constant independent of the rest of the extragalactic distance scale. In the next decade it is quite likely that surveys will begin to turn up significant numbers of these objects at z ~ 0.5 and, therefore, the possibility exists that SNII will be able to make a contribution to the measurement of cosmological parameters beyond the Hubble Constant. Since SNII do not have the precision of the SNIa (next section) and are significantly harder to measure, they will not replace the SNIa but will remain an independent class of objects which have the potential to confirm the interesting results that have emerged from the SNIa studies.

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