We study the correlation between far-infared/submm dust emission and atomic gas column density in order to derive the properties of the high Galactic latitude , low density , Milky Way cirrus in the foreground of the Virgo cluster of galaxies .
Dust emission maps from 60 to 850 \mu m are obtained from SPIRE observations carried out within the Herschel Virgo Cluster Survey , complemented by IRAS-IRIS and Planck -HFI maps .
Data from the Arecibo legacy Fast ALFA Survey is used to derive atomic gas column densities for two broad velocity components , low and intermediate velocity clouds .
Dust emissivities are derived for each gas component and each far-infared/submm band .
For the low velocity clouds , we measure an average emissivity \epsilon ^ { \mathrm { LVC } } _ { \nu } = ( 0.79 \pm 0.08 ) \times 10 ^ { -20 } MJy sr ^ { -1 } cm ^ { 2 } at 250 \mu m. After fitting a modified blackbody to the available bands , we estimated a dust absorption cross-section \tau ^ { \mathrm { LVC } } _ { \nu } / { N _ { H \textsc { i } } } = ( 0.49 \pm 0.13 ) \times 10 ^ { -25 } cm ^ { 2 } H ^ { -1 } at 250 \mu m ( with dust temperature T = 20.4 \pm 1.5 K and spectral index \beta = 1.53 \pm 0.17 ) .
The results are in excellent agreement with those obtained by Planck over a much larger coverage of the high Galactic latitude cirrus ( 50 % of the sky vs 0.2 % in our work ) .
For dust associated with intermediate velocity gas , we confirm earlier Planck results and find a higher temperature and lower emissivity and cross-section .
After subtracting the modelled components , we find regions at scales smaller than 20 \arcmin where the residuals deviate significantly from the average , cosmic-infrared-background dominated , scatter .
These large residuals are most likely due to local variations in the cirrus dust properties ( and/or the dust/atomic-gas correlation ) or to high-latitude molecular clouds with average N _ { \mathrm { H } _ { 2 } } \lesssim 10 ^ { 20 } cm ^ { -2 } .
We find no conclusive evidence for intracluster dust emission in Virgo .