In this paper we present the results of the first low frequency all-sky search of continuous gravitational wave signals conducted on Virgo VSR2 and VSR4 data .
The search covered the full sky , a frequency range between 20 Hz and 128 Hz with a range of spin-down between -1.0 \times 10 ^ { -10 } Hz/s and +1.5 \times 10 ^ { -11 } Hz/s , and was based on a hierarchical approach .
The starting point was a set of short Fast Fourier Transforms ( FFT ) , of length 8192 seconds , built from the calibrated strain data .
Aggressive data cleaning , both in the time and frequency domains , has been done in order to remove , as much as possible , the effect of disturbances of instrumental origin .
On each dataset a number of candidates has been selected , using the FrequencyHough transform in an incoherent step .
Only coincident candidates among VSR2 and VSR4 have been examined in order to strongly reduce the false alarm probability , and the most significant candidates have been selected .
The criteria we have used for candidate selection and for the coincidence step greatly reduce the harmful effect of large instrumental artifacts .
Selected candidates have been subject to a follow-up by constructing a new set of longer FFTs followed by a further incoherent analysis , still based on the FrequencyHough transform .
No evidence for continuous gravitational wave signals was found , therefore we have set a population-based joint VSR2-VSR4 90 \% confidence level upper limit on the dimensionless gravitational wave strain in the frequency range between 20 Hz and 128 Hz .
This is the first all-sky search for continuous gravitational waves conducted at frequencies below 50 Hz .
We set upper limits in the range between about 10 ^ { -24 } and 2 \times 10 ^ { -23 } at most frequencies .
Our upper limits on signal strain show an improvement of up to a factor of \sim 2 with respect to the results of previous all-sky searches at frequencies below 80 ~ { } \mathrm { Hz } .