4U1700-37

5 The compact companion

Figure 7: Mass distribution for neutron stars and black holes (after Charles 1998). Neutron star masses are from Ash et al. (1999), Barziv et al. (2001), van Kerkwijk et al. (1995) and Thorsett & Chakrabarty (1999). Black hole masses provided by Charles (priv. comm.). Error bars for systems other than 4U1700-37 are 1 sigma errors; see Sect. 3 for a discussion of the errors associated with the mass of 4U1700-37 but note that the probability of $M<2~M_{\odot}$ is less than 3.5 per cent, and no trials results in $M<1.65~M_{\odot}$.

At present mass determinations exist for 36 compact objects, of which 21 are neutron stars and the remainder black hole candidates (Fig. 7). Thorsett & Chakrabarthy (1999) found that the masses of neutron stars are clustered in a remarkably narrow range (mean of 1.35 $M_{\odot }$ and a standard deviation of 0.04 $M_{\odot }$). However, recent analysis of Vela X-1 by Barziv et al. (2001) suggests that the pulsar has a mass of 1.87 ^+0.23_-0.17 $M_{\odot }$, while Orosz & Kuulkers (1999) find a mass of $1.78 \pm 0.23~M_{\odot}$ for Cygnus X-2 (however Titarchuk & Shaposhnikov 2002 have recently proposed $M=1.44 \pm 0.06~M_{\odot}$ on the basis of Type-I X-ray bursts).

Based on assumptions about the origin of kilohertz quasi-periodic oscillations Zhang et al. (1997) suggest that several LMXBs may also contain massive ($\sim$2 $M_{\odot }$) neutron stars, resulting from the accretion of substantial amounts of material over long (10⁸ yrs) periods of time. However their putative descendants, radio pulsar+white dwarf binaries, provide no evidence for massive neutron stars (Barziv et al. 2001). The same is true for the Be/X-ray binaries, which have evolved from lower mass systems than the OB-supergiant HMXBs. Only in the latter systems evidence has been found for massive neutron stars and black hole candidates.

Masses for a number of black hole candidates have also been determined; lower limits to their masses comfortably exceed 3 $M_{\odot }$. Indeed several objects appear to have masses $\ga$10 $M_{\odot }$ (e.g. $14\pm 4~M_{\odot}$ for GRS 1915+105; Greiner et al. 2001), with most typically $\ga$6 $M_{\odot }$. At present the binary system with the lowest mass candidate black hole is Nova Vel ( $4.4~M_{\odot}$; Fillipenko et al. 1999).

Given that the mass of the compact object in 4U1700-37 lies outside the present observational range for both neutron stars and candidate black holes, is it possible to increase/decrease the mass of the compact object such that it is consistent with either type of object? For the case of a circular orbit we find no solutions consistent with $M_{x} \ga 4.4$ $M_{\odot }$. Very eccentric orbital solutions do allow values of M_x in this range although we note there is no physical motivation for them. Such solutions imply values of $M_{\rm o}$ greatly in excess of 100 $M_{\odot }$, well above current evolutionary predictions for the mass of an O6.5 Iaf+ star. Stars with masses in excess of 100 $M_{\odot }$ are instead expected to evolve to H depleted WR stars via a H rich pseudo-WNL phase where their powerful stellar winds mimic the spectra of more (chemically) evolved stars of lower masses.

Such a large mass would also be inconsistent with the constraints imposed by the surface gravity (Sect. 2.2) and the relationship between stellar mass and the terminal wind velocity. Finally the result would imply that even very massive stars (given that the initial mass of the SN progenitor had to be significantly in excess of the present mass of HD 153919) leave relatively low mass remnants post supernova, presenting significant problems for the origin of heavy (>10 $M_{\odot }$) black holes such as e.g. Cyg X-1. Therefore we conclude that M_x appears to be inconsistent with the range of masses of known black hole candidates.

Given the stringent lower limits derived in Sect. 3 it also appears difficult to bring the mass of the compact object into line with the range of masses found by Thorsett & Chakrabarthy (1999). Inspection of the evolutionary tracks in Fig. 6 suggest that stars with initial masses of the order of 60 $M_{\odot }$ initially evolve redwards before returning bluewards after undergoing significant mass loss, most likely during an LBV phase. While we note that the behaviour of stars in this short lived phase is very uncertain it is unlikely that we could be observing HD 153919 after such an excursion, since we would expect significant chemical enrichment - the H rich mantle having been lost - which is not observed. Likewise, the mass constraint imposed by the determination of the surface gravity also appears to exclude this scenario.

Furthermore, such a low value for $M_{\rm o}$ and M_x would reintroduce the problem of HD 153919 being undermassive for its spectral type by a factor $\ga$2. While the primaries in some HMXB systems are found to be undermassive (e.g. Cen X-3 and LMC X-4; Kaper 2001) this is attributed to mass loss via RLOF - wind fed systems do not show this effect (Kaper 2001). Given that 4U1700-37 is currently a wind fed system and is yet to evolve into a RLOF system this could not explain such a mass discrepancy. Indeed, given the evolutionary constraints imposed by the present orbital period it is likely that no significant mass transfer has occured onto HD 153919 during its lifetime, and it will have evolved as if it were an isolated star.

5.1 Implications of an intermediate mass

If we accept $M_x =2.44\pm 0.27~M_{\odot}$ - as implied by the simulations - the nature of the compact companion remains uncertain. Conflicting claims as to the nature of the object have been made on the basis of the X-ray spectrum of 4U1700-37 (Sect. 1). While we cannot discriminate between the twin possibilities of massive neutron star or low mass black hole from our present measurements we note that consideration of the masses of both components of the binary appear to exclude the possibility that stars with masses of $\sim$60 $M_{\odot }$ can produce 5-10 $M_{\odot }$ black holes via case A or B evolution.

If the compact object in 4U1700-37 is a black hole it confirms Brown et al.'s prediction of the existence of "low mass black holes'' (based on their "soft'' equation of state, Brown et al. 1996), while if the object is a neutron star the high mass would severely constrain the equation of state of matter at supra-nuclear densities.

The relationship between the mass of a neutron star and its central density is calculated by integration of the Tolman-Oppenheimer-Volkoff (TOV) equation (Oppenheimer & Volkoff 1939) which is the relativistic expression for hydrostatic equilibrium. In order to perform the integration it is neccesary to understand the equation of state of the degenerate nuclear matter in the star.

Because of their non-perturbative nature, strong interactions between nuclei are extremely difficult to calculate even under normal conditions. However, there are several models of the internuclear potential in the literature which have achieved much success in modelling nuclei e.g. Stoks et al. (1994), Wiringa et al. (1995) and Machleidt et al. (1996). One of the most successful and up to date of these models has been applied to the neutron star equation of state by Akmal et al. (1998) yielding a maximum mass of between 2.2 and 2.4 $M_{\odot }$ for a neutron star made completely of normal nuclear matter.

There is also the possibility of a QCD phase transition occuring in the centre of the neutron star. The large chemical potential has a similar effect to a large temperature on the QCD coupling constant. Consequently the interquark coupling can be reduced to the point where deconfinement occurs and nuclei dissolve into quark matter. The presence of quark matter has the effect of softening the equation of state which leads to a lower possible maximum mass for the neutron star. The energy scale at which deconfinement occurs can be parameterised by the QCD bag constant B, a phenomenological parameter representing the difference in energy density between the vacua of hadronic and quark matter ( $B\approx 120$-200 MeV fm^-3). Inclusion of a phase transition to such a mixed state reduces the maximum mass of the neutron star to $\sim$2 $M_{\odot }$ for B=200MeV fm^-3 and $\sim$1.9 $M_{\odot }$ for B=122 MeV fm^-3(Akmal et al. 1998).

If the neutron is rotating rapidly, the TOV equation ceases to be a valid approximation and one must drop the assumption of spherical symmetry in the metric. The effect of the rotation will increase the allowed mass of the neutron star as one might expect, but it is shown (Heiselberg & Hjorth-Jensen 1999) that even with rotation one cannot obtain a neutron star with a mass much higher than those listed above without using an equation of state so stiff that the sound speed in the neutron-star interior becomes superluminal.

To summarize this subsection, state of the art models for nuclear equations of state which include the effects of three nucleon interactions marginally allow the existence of a 2.4 $M_{\odot }$neutron star. However, the existence of such a star would place severe constraints upon the onset of new physics at high hadronic densities. For instance, in the model where a quark matter core is expected to develop, the bag constant B would have to be considerably larger than 200 MeV fm^-3 in order for such a star to be viable.

4U1700-37